The culture of exercise/fitness suffers from a motivation (and discipline) problem. Sports turn it around and make it actually fun, lessening the need for those.
Despite the the media and blogs and forums talking incredibly a lot about exercise/fitness, not everybody is motivated to do it. Of those who do, some hate it and will stop once the motivation runs out. Some try to go from motivation to discipline to fight it, but it is an uphill fight: why exercise/fitness cannot be fun you want to do, not a second grinding job you must do? The need for discipline or motivation suggests it is no fun. Some people try to turn boring exercise into a game with e.g. Fitocracy. However there is an old and time-tested way to do it: actual sports, not necessarily competitively.
The approximate reason
Sports coaches have used strength and cardio training as a part of their toolbox since a long time. Exercise/fitness looks a lot like basically taking out this aspect of sport trainings and leaving out the rest. 
However by doing so we lose three important motivators:
1) Playing sports - not necessarily on competitive levels! - is fun (for some at least), and in itself they work as cardio or HIIT training. Think playing soccer or martial arts sparring or playing tennis, hard effort and rest intervals, quite HIIT-ish, and HIIT training seems to confer similar benefits to weight lifting - it is usually considered anaerobic.
2) When doing exercise/fitness our motivation is usually to be healthier, feel better, and be sexier. When doing strength or cardio as part of a sports coaching / training, we have a fourth motivator: to be actually better at playing at that sport. One big issue with exercise/fitness is that in an comfy urban life we do not actually use strength or endurance, and this is a huge demotivator (for me at least, I suspect others too): it feels a bit like growing a pretty but useless third leg. Why be stronger, when spending that time studying is more efficient for real world success? (The worst offender is the CrossFit movement: it makes you fit for all kinds of purposes, most of which you will never pursue!) Health, mood and sexiness are good reasons, but still doing a sport where we can use strength or endurance for some real goal makes a whole world of difference - for me at least. What do you think your "inner caveman" wants: to e.g. sprint because it makes him healthier, sexier and puts him in a better mood or to actually catch that deer, which means: to motivate your "inner caveman", you better find yourself some actual deer to catch, some actual use-goal to pursue, and this is why sports work: the goal is to win a friendly match or something similar. Remember: to be fit means to be fit for something, and you need a something.
3) Commands and camaraderie. When the coach yells 25 push-ups and 20 people hit the ground and do it is a very different motivator than just bargaining with yourself to do it at home or to do a bit more before going home from the gym. Yes, you can hire personal trainers or find training buddies. But this is IMHO less ingrained (at least in Mitteleuropa) in the culture of fitness/exercise than in actual sports. Group coaching/training has a military feel to it, and militaries tend to be efficient at figuring these things out, for them it is a life and death issue.
Let's stop and reflect a bit on the weirdness of it all... for example people are using apps like Fitocracy and HabitRPG to turn their boring exercises into an RPG videogame, to gain XP and level up... when in reality martial arts belt tests have always been precisely that. Less formally, but rankings exist in sports all the way, for example just training and for fun -> allowed to play training matches against the other half of our team -> allowed to play training matches with other teams -> allowed to play in friendly matches and so on, or in boxing sandbag -> mittens -> light sparring -> full force sparring -> training match -> match or for Alpine skiers being allowed to go to green/blue/red/black pistes.
Sports are already an RPG, so why do we had to take strength and cardio training out of sports and just do these exercises without doing the sport part, then finding out it is boring and demotivating and turning it into an RPG again? Does this even makes sense? And if not, why did it ever happen so?
Why it happened so 1.
For busy and highly motivated people, exercise/fitness works. If 2 hours of sports coaching means 0.5 hour strength, 0.5 hour cardio, 0.5 hour technique and 0.5 playing, they may as well take the first hour and leave the second i.e. go to a gym, not coaching. It works if you are Elon Musk or anywhere close to making someone like him your goal model.
It obviously does not work well for people who are in this sense more typical i.e. more free time to kill (goals do not fill out time) but less willpower/motivation/discipline. I think fitness/exercise culture was generated by those highly succesful people. Esp. by fitness trainers who are almost fanatical about it in their own lives.
Why it happened so 2.
When I say "sports" a lot of people here "competing". "Being good enough to compete", "investing enough time to compete". They simply don't find anywhere near them half-serious, kinda-recreational sports opportunities where they are still pushed fairly hard by the coach, but they are not expected to compete much and not expected to be good at it.
To put it differently, we should draw a clear line between competitive sports where if you are like an "employee" of the coach and if not good enough the coach simply does not want you in his team, and recreational sports where you are a customer of the coach/trainer, you pay him to make you better at the sport than you previously were, no matter how bad that previous level was. I am talking about the second.
In Europe, anecdotally, without statistical evidence at hand, recreationally coached sports unions (Vereins in German) seems to be on the decline, body-building gyms attracting people away. Perhaps in America the whole culture is so competitive that they were never really a thing?
However AFAIK many recreationally coached sports are still available. We should make a full list in the comments but I can find two examples:
- Tennis and squash. However you will not be pushed much towards strength traning. But still, you get to the point where you want to hit the ball harder and it motivates you for strength training.
- Martial arts. Choose any you like, because liking is more important for the beginning than benefits, and it is not a final choice, learning multiple ones and later mixing them is the idea behind MMA. If and only if you think the art you chose is too easy on the strength training side, not pushing you enough, look towards BJJ, boxing or MMA, they seem to be the "buffest" ones around i.e. where coashes push you to strength training the most.
Why it happened so 3.
Back in 1960's or so obesity was not really an issue (less than half, PDF) like today is globally, or at least people were not very conscious about it. Some people did sports but otherwise exercise and fitness flew below the radar. It was roughly in in the later 70's, early 80's when people started to pay attention to exercise and fitness. When Arnold's Pumping Iron popularized bod body building in 1977, it was not mainly about making obese men and women thinner but about making thin, scrawny men more muscular. The media bought into this new body image (fun homework idea: how Stallone went buffer during the Rocky series, reflecting the expectations of the media or the public, or how Spiderman comics changed 1960 to 1990). In 1982 Jane Fonda launched the aerobic movement, this was more directed on making overweight women thinner. This is roughly the recent origins of the fitness/exercise culture.
As of today, at least if fitness.reddit.com is a reliable predictor of opinions, "Arnold" won, "Jane" lost i.e. todays idea of fitness is more based on weight lifting / body building, including women, than aerobic in the Jane Fonda sense of the term. There are good scientific reasons for it, in a nutshell: weight lifting's effect on metabolic rate, insuline sensitivity, leptin sensitivity, HGH and T, all having an effect on fat, and both building muscles and having them around having an effect on fat (source: book).
The issue is, people see sports like playing volleyball closer to "Jane" than "Arnold". With "Jane" losing to "Arnold", not only aerobic-cardio lost to weight training, but doing actual sports lost to going to gyms.
But let's not forget that the Arnoldian Way was originally about not being scrawny, not about not being fat, which brings us to:
Another weird factor
While todays main problem is obesity; popular, Arnoldian fitness culture is originally based on gaining muscle, not on losing fat. While gaining muscle is an excellent way to lose fat, probably the best way if you have the motivation/discipline for it (reasons see in above ref. book), the simple truth is that if a fat guy or gal just plays basketball 3 x 1 hours a week, he or she will gain muscle simply by throwing his or her heavy body around, with high enough body weight much of "cardio" doubles as strength training. For the skeptical, do you cardio while a petite woman is sitting on top of you - that is what it is like for fat people.
Example: scrawny, ectomorph, hardgainer lifters often complain about calves being hard to grow. My cousin's "secret tip" for brutal calves is 1) be an obese 140 kg man 2) play soccer once a week. (Don't even think about suddenly starting playing soccer if you are that obese! Rather he went from 70kg to 140 during 10 years while playing soccer once a week and basically his joints gradually adapted to the weight!)
If a fat man or woman needs motivation or discipline to go to the gym to do boring gym stuff, but loves to play volleyball and has a chance to play 3 x 1 hours a week, he or she will put on muscle. After 3 months, being in a good, proud, and enthusiastic mood about being an active person now, he or she can easily add a push-up program (with handles, better for wrists, this but repeat every week 3-4 times over) on the rest of the days will result in respectable shoulders, pecs, arms. But the order of things is important here, first do enjoyable activity, then leverage the good feels and pride into less enjoyable and more efficient ones!
Frankly most fitness trainers, bloggers don't really understand this. Typcially the are ex-scrawny guys desperate to gain, who consider in our example volleyball a just cardio (it is with 60-80kg but with 130kg it gives you quite some leg muscles), and push-ups not very efficient (again at 60-80 kg not, at 130 kg yes, ask a petite woman to sit on your back and try it that way and suddenly you will respect it more!).
The expanse of the problem
How widespread is the problem I am describing? Well, even here on LW, an otherwise excellently written article ignores the motivation and fun angle and talks about starting with a body weight routine then graduating to weight lifting and cardio, ignoring that 1) for many people these are boring activities 2) without having a sport goal, we do not use strength or endurance in a comfy urban existence and simply health, sexiness and good mood are not always strong motivators. I think the article can be "excused" - quotes because I am not actually making a judgement here, hence no excuse is needed: it is an excellent article coming from a fitness / exercise culture where apparently EVERYBODY has this blind spot, I would never think about singling out the author and blaming him for it! -, anyway, this article can be explained by being written for typical "Bay Area Rationalists", wannabee Elon Musks who already have a lot of motivation and willpower and discipline but not enough free time, having a lot of goals. So they want to be time-efficient, not fun-efficient.
But yeah, for Average Guy or Gal where the opportunity cost is less time killed in front of the TV, fun-efficient is more important than time-efficient. Making it twice as long but twice as fun makes them want to do it more. And hence it must be sports.
If you are content with your exercise habits, you don' have a problem or not one this article can solve.
If your problem is that you are thin, scrawny (NOT skinnyfat), ectomorph, hardgainer, I cannot help you much: you need weight lifting / body building / advanced gymnastics, the only possible way out from gym culture I can think of is rock or wall or boulder climbing or parkour, basically figure out fun ways to efficiently use your low body weight as a resistance. But other than that no news here. Except one, but that would be better discussed in a separate article: why are many young men unhappy with being thinly athletic? Media image, surely, but I have an hunch it is not about looking better but about looking and feeling more respectable, and this may be a different kind of problem. I see 17 years old guys desperate to put on muscle not just to look better but also in order to be treated not like a boy but like a respectable adult man. And I see 40 years old guys who are more like, if I am not fat and have the cardio endurance to play tennis then I am OK, I am already a "someone", I have nothing to prove. Do you see anything like this? But I think this requires a separate article to discuss.
If you are fat (or skinnyfat), and struggle with the motivation / discipline to exercise, I can help you. Forget fitness and exercise and start a sport you like.
Algorithm for deciding what sport you like
1) Do you watch any sports in TV or play them in videogames?
2) Do you watch action movies that involve one kind of fighting or another, or play suchlike in videogames? If yes, martial arts, for starters, an unarmed one, but let's not ignore the magnetic effect medieval longsword fighting tends to have on "geeks", quite possibly the only truly likable sport for RPG or fantasy or history fans. Watch this then Google "HEMA mycity" or even "Liechtenauer mycity" (He was the originator of that late Medieval tradition that produced the most often used longsword fencing books and longsword fighting clubs often mention the Liechtenauer tradition / school on their site. Other good choices: Fiore, Marozzo.)
3) Failing these, you may not want to do a sport as such, but maybe you still want to be with friends or coworkers who do it, and enjoy doing it with them, so ask around.
4) Whatever is close to your home or work.
5) If nothing helps and you are really clueless martial arts. You are an animal. There is _some_ size of fight in every dog.
6) If you are disabled, your choices are limited, from none at all to wheelchair basketball.
The motivation problem solving itself
The important thing is that you don't need motivation to do the sport, you just need the motivation to drag your butt to the training session, basically to "show up". Then you can just surrender your will to the trainer. Be a remote controlled robot, a zombie without will, executing the will of the trainer, Kadavergehorsam. This will get you through the first, sucky part of the session, cardio and strength training. Then the technique training will be more interesing and you will be glad for the rest, and finally you ge to play, spar, do the actual sport, enjoy the fun, and this sends you home with good feelings, eager for the next session. Most trainers I know in martial arts or soccer use this structure: warm up with cardio, do strength, do technique which doubles as a rest, and finally play and enjoy. This because it makes sense for the body, but also it is psychologically motivating, go through the sucky parts and then do the rewarding parts. Actual sports trainers seem to care more about motivation and psychology than the blogs of fitness trainers...
Oh BTW I purposefully formulated the robot-zombie-Kadavergehorsam part so that a lot of people shudder reading it and feel bad about it: 21st century people tend to value their autonomy... but it is a thing people like me need to face and better sooner than later. You need cardio and strength, there are some sports you can just warm up and then play it, but still you need to warm up and for an untrained person that leads to some panting. So there are only two ways: you want to do cardio and strength, or you don't but you surrender your will to someone who wants you to do it. How else you think your body will do it? It needs a control unit, and you have two choices: your will (motivation, discipline) or the will of someone else. If you hate yourself for your laziness, and I do, surrendering to someone you actually respect does not sound that bad once you get past the idea that it is in this age of autonomy "weird".
Another rule I want to recommend is one habit at one time. Exercise routines consisting of 4-5 different exercises are IMHO harder to stick to, it is easier to obssess about one thing. For this reason, if you started your sport, for a few weeks or months until you feel it is an organic feature of your life you would miss if you stopped, don't try other exercises! Keep yourself back, hold back on your newfound enthusiasm! It is similar to Pavel Tsatsouline saying (cannot find the source, sorry) to not train to failure, stop a training before you are exhausted, stop a training when there is still some hunger in you for more, so that you are motivated to do it the next time. The same way, if in the first weeks your enthusiasm makes you hunger for more, just stay hungry, do not satisfy it, let this motivation carry you until your sport is an ingrained habit.
The next step
Okay, so you are doing a sport 2-3 times a week for 2-3 months now, it is an ingrained habit now, you are getting in a better mood, being more proud of yourself, and you feel you can now do more. Look into what kind of muscles can you use for your sport, and what kind of muscles your sport does not develop enough! The answer is very often this: you jump around on your feet all the time, gravity is training your legs all right during your sport (again, I am talking about fat people, jumping around with 130 kg is different than with 65 kg), you are probably twisting and turning (training the abs), but your arms, upper body is not trained enough, and yet precisely this is what you need to hit a ball forcefully, throw a ball forcefull, or to throw a punch. In other words, for many sports, time to do push-ups at home on the non-training days. This trains the right kind of muscles for this.
Two things to consider here. One, I am not talking about a bodyweight routine: only push-ups. One habit, one obsession at one time! Make the choice simple for your brain: either I am at rest, or down the floor going up and down, no third choice! This is the secret for habit forming for me: don't fatigue your brain with having to choose to do 4-5 things, just 1 thing! Second, I am recommending to start the push-ups only months after you started a fun sport, not before, you will have way more motivation that way: now it is not just about health, sexiness and mood but about actually using that kind of strength for something, plus you are in a better mood and you have more self-respect, you are more in a can-do, want-to mood! As above: with handles, better for wrists, this but repeat every week 3-4 times over if you are fat.
From that on - you are on your own. Once you hit the 100 mark, and do your sport 3 times a week, and all this coupled with a good diet, you probably have everything you need psychologically to go on your own way.
And be aware that we knew all this in the 1960's or so. People - well, at least boys - were pushed to do sports. I hope we can bring it back, and for people who do not have unusual amounts of motivation or discipline, body-building or weight-lifting will not be seen as the alternative to being a couch potato, but rather both as separate, special sports for those who specifically like them, and for everybody else just a part of their sport training that aims, primarily, at being fit to play or spar or occasionally compete in stuff that is fun.
For people with alcohol problems
You probably want to both stop drinking and start a sport or exercise routine. Being hung over is a huge exercise demotivator, and exercise makes it easier to deal with the depression / bad mood of cravings. Where to start? For me, stopping drinking then starting sports or exercising did not work, I could not deal with the bad mood. Joining a boxing gym while still drinking, dragging my hung-over ass to the session, using my own volition only to go there than handing it over to the trainer, cursing myself while the trainer made me sweat and burp it out, yet being in a better mood the day after and feeling more proud of myself and not like a worthless piece of feces, made me - fingers crossed - gather the strenght to quit. It is only a few days ago but I mention it as a form of public commitment. So if stopping first then doing sports or exercising did not work, the other way around may still work for you, and remember, with a coached recreational sport, you don't need to have the willpower, motivation or discipline to do it! You just need enough motivation to show up, and then simply you surrender your will to the trainer, you need to make no more choices.
Adamzerner makes a good point about how skill differences cause problems in team sports, suggesting, to me, to better start with an individual / pair one practiced in group settings (martial arts, tennis or squash courses with other people, dancing and so on) at least until your motoric skills, coordination, speed, cardio picks up.
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 Not actually historically / chronologically so.
 Yes, weight lifting, body building, running are actual sports as well, but they are used by many, many more people than those who wish to compete in them either for sports training or just exercise/fitness.