On the "why" question...

Let me start by interrogating the monogamy rule. What exactly is the rule?

Is it that certain forms of physical touching are against the rules? [Handshakes?—I've heard many Muslims do consider that out of bounds. Hugs? Kisses on the cheek? Rubbing sunscreen onto their back?] How about looking without touching? [A wayward glance? Is there a time limit? Depending on how clothed they are? If they choose to dress sexily, what obligations does this impose on you to avoid them?] And presumably there are exceptions for medical procedures. [Or are there? Maybe you can insist on same-sex doctors.]
Or is it more like "Don't engage in behavior with the intent of sexual gratification with anyone but your partner?" [How about porn and masturbation? What if someone flirts with me and I play along and I enjoy it? What if you think they're flirting with me and I disagree?]
Is it "Flatter my desire to be the exclusive target of your sexual desires"? [Does this imply lying about not finding celebrities hot, or a don't-ask-don't-tell policy, or attempts at self-modification and/or self-deception? "Well, 25-year-old Scarlett Johansson isn't my husband's coworker, and if she were she wouldn't just throw herself at him, so I can forget about such unrealistic threats." Does that mean, if your husband gets fitter and hotter, you'll find this threatening?]
Or is it, perhaps, "If you're asking these questions, you're obviously not suited for a relationship with me"? [Which I have been told.]

I don't see good answers. For the exclusively behavior-focused rules, any line you draw seems probably either overly restrictive, or there are some people who would derive sexual pleasure from what is allowed and that probably defeats the purpose—or possibly both. And it seems like, in practice, people draw the line in fairly different places, for unclear reasons; it seems arbitrary and stupid. Unless I take it to be a consequence of the more intent-focused or outcome-focused rules, which have their own problems—tending to strike me as either super-restrictive, a source of arguments and self-deception, and/or unrealistic.

Next, putting that aside. Even supposing you're in a perfect monogamous setup, where both of you only have eyes for each other... how long can you honestly promise that will last? Googling says that 20% of marriages end in divorce within 10 years. A British survey of those that were together 10+ years said that 20% of them had cheated. I haven't found a source with numbers, but I think there are also lots of couples who, though they stay together, they rarely or never have sex anymore.

Things happen. You and your partner may change, and one may become no longer attractive to the other. Can you really, honestly promise that won't happen?

Maybe you think you have specific information about yourselves. Is a promise of "There's a 90% chance we'll still be great together in 10 years" emotionally satisfying? What about 80%? 60%? It may be a worthwhile bet, but the thing people seem to want is "I'll only ever love you / be attracted to you", and that strikes me as either a short-term honeymoon effect, self-deception, or perhaps a condemnation of one's own sexual market value.

Next, there's the question of why you would want those restrictions. First, coming from economics, I've learned to be extremely skeptical of arguments for why it's a moral imperative to restrict competition. Second, the way I interpret "I love my partner", one of the consequences is "If there's a thing that makes her happy or otherwise helps her, and makes no difference to me, then that's a good thing"—more generally, her happiness and well-being should factor into my utility function.

What exactly is it that people object to, in their partner having sex with someone else? Interrogate that. There are potentially valid concerns in there; isolate them.

Scared that she'll run off with the guy and leave you? Fair. Now imagine you're confident she's not going to do that. (If necessary, imagine you have a marriage contract where if she does that, she forfeits $1M, and/or her reputation, or whatever.)
Scared that she'll bring home STDs or an unwanted pregnancy? Fair. Now suppose the guy is screened for STDs and they're using multiple forms of protection.
Scared that the guy will abuse her? Fair. Now suppose you know the guy and he has an impeccable history, and meanwhile she knows she can come to you with any complaints.
Scared that she'll always go to him when she's horny, and stop having sex with you? Possibly fair. In the general case this should be negotiated; but here, let's suppose we're considering what she's allowed to do specifically when you're out of town for a week.
Scared that she'll discover the guy is a much better match for her than you and want to leave you [separately from the question of whether she does leave you]? Well, erm, if that's true, do you think it's morally proper for the relationship to require her to be stuck with just you indefinitely?
- If you have kids already, then maybe she'll decide that keeping an intact family environment is more important than whatever delta in mate quality she can get from him over you. Or maybe she'll decide the latter is more important, and screw the family? Would you have married someone with that set of priorities?
- If you don't have kids or any other big commitment holding you together, well...
  - If the thing attracting her to the guy is shallow, then surely she'll figure that out after not too long.
    - If, during that time, she completely abandons and mistreats you, then I'd say she wasn't good relationship material.
    - On the other hand, if it means she's away from you just a few days a week... is that so bad?
      - If, during that time, you're wracked with anxiety at the prospect of her possibly deciding to leave you... then how confident were you in the first place that you and she were a good match?
        If you think you're a good match, but also think she'll likely make a bad decision based on his shallow appeal and whatnot and you won't be able to persuade her otherwise... then remind me why you think she's a good match for you?
  - If she's truly long-term significantly better off with him, then... you really want to keep her tied to you forever? Are you proud of doing that?
    - Or would you want her to mindfuck herself into thinking that, no, she really is better off with you? And not tell you she did that, so you can keep your own conscience fully clear? Jesus Christ.

Ultimately, you can separate the "jealousy" concerns into "valid" vs "not something you'd endorse upon reflection", and I think the "valid" concerns can frequently (not always) be addressed, so there's a decent-sized space of possibilities where sticking to monogamy would mean denying your partner something good for no endorsed reason. Which I consider beneath me.

For having children, I think something resembling marriage is a good idea. But I think the rules that make sense for it are along the lines of "don't bring home STDs, unwanted pregnancies, or serious drama; don't abandon the family; maintain some agreed-upon level of romantic activity with your partner; don't get involved with people who will try to persuade you to break these rules [this probably shouldn't need to be a rule]", and that monogamy is a suboptimal approximation to the ideal.

For simple pleasure... Well, "do what you want, subject to other people's rights and the agreements you make with them" seems like the thing; one needs a strong argument to say otherwise. There are probably problems with the overall market; people say the top few men end up with lots of women, and the bottom x% of men are left out in the cold. Polyandry might help with that. Either way, technological alternatives to sex are making that matter less, and I think this will continue. That seems fine to me.

There are people who say that if men have sex substitutes, then they'll be (or already are) less motivated to make themselves economically productive to attract women, which will be bad, and therefore we should ban sex substitutes, like the upcoming sex robots and perhaps today's porn and possibly more stuff. I humbly suggest that such people should be forcibly addicted to cocaine, and have Martin Shkreli sell their fix to them at whatever price he chooses; surely that will motivate them to power the economy. More seriously, it's an infringement on general freedom, and the fact that it works by setting up a bunch of people for serious emotional distress by making it difficult and uncertain for them to fulfill a strong biological need ... strikes me as reprehensible.

For "building a life together"... if not for the sex/romance aspect, you could do this with a very close lifelong friend. Some people do. It would be cool if this happened more often. But anyway. I think there's a set of people who think, "I'd like to build a life with this person... But I worry that, at some point, she'll lose interest in sex, and that I'll be miserable. I won't want to leave her, but I might not be able to tolerate staying." Some of the /r/DeadBedrooms posts describe that exact outcome. But if the relationship allows getting sex elsewhere, that can let it survive that problem.