(Disclaimer: The following perspectives are based in my experience with policy debate which is fifteen years out of date. The meta-level point should stand regardless.)
If you are not familiar with U.S. high school debate club ("policy debate" or "cross-examination debate"), here is the gist of it: two teams argue over a topic, and a judge determines who has won.
When we get into the details, there are a lot of problems with the format. Almost everything wrong with policy debate appears in this image:
This is a "flowsheet", and it is used to track threads of argument between the successive epochs of the debate round. The judge and the debators keep their own flowsheets to make sense of what's going on.
I am sure that there is a skillful, positive way of using flowsheets, but I have never seen it used in any way other than the following:
After the Affirmative side lays out their proposal, the Negative throws out a shotgun blast of more-or-less applicable arguments drawn from their giant plastic tote containing pre-prepared arguments. The Affirmative then counters the Negative's arguments using their own set of pre-prepared counter-arguments. Crucially, all of the Negative arguments must be met. Look at the Flowsheet image again, and notice how each "argument" has an arrow which carries it rightward. If any of these arrows make it to the right side of the page - the end of the round - without being addressed, then the judge will typically consider the round to be won by the side who originated that arrow.
So it doesn't actually matter if an argument receives a good counterargument. It only matters that the other team has addressed it appropriately.
Furthermore, merely addressing the argument with ad hoc counterargument is usually not sufficient. If the Negative makes an argument which contains five separate logical fallacies, and the Affirmative points all of these out and then moves on, the judge may not actually consider the Negative argument to have been refuted - because the Affirmative did not cite any Evidence.
Evidence, in policy debate, is a term of art, and it means "something printed out from a reputable media source and taped onto a notecard." You can't say "water is wet" in a policy debate round without backing it up with a notecard quoting a news source corroborating the wetness of water. So, skillfully pointing out those logical fallacies is meaningless if you don't have the Evidence to back up your claims.
Skilled policy debators can be very good - impressively good - at the mental operations of juggling all these argument threads in their mind and pulling out the appropriate notecard evidence. My entire social circle in high school was composed of serious debators, many of whom were brilliant at it.
Having observed some of these people for the ensuing decade, I sometimes suspect that policy debate damaged their reasoning ability. If I were entirely simplistic about it, I would say that policy debate has destroyed their ability to think and argue rationally. These people essentially still argue the same way, by mental flowsheet, acting as though argument can proceed only via notecard exchange. If they have addressed an argument, they consider it to be refuted. If they question an argument's source ("Wikipedia? Really?"), they consider it to be refuted. If their opponent ignores one of their inconsequential points, they consider themselves to have won. They do not seem to possess any faculty for discerning whether or not one argument actually defeats another. It is the equivalent of a child whose vision of sword fighting is focused on the clicking together of the blades, with no consideration for the intent of cutting the enemy.
Policy debate is to actual healthy argumentation as checkers is to actual warfare. Key components of the object being gamified are ignored or abstracted away until the remaining simulacrum no longer represents the original.
I actually see Notecard Logic and Flowsheet Logic everywhere. That's why I have to back off from my assertion that policy debate destroyed anybody's reasoning ability - I think it may have simply reinforced and hypertrophied the default human argumentation algorithm.
Flowsheet Logic is the tendency to think that you have defeated an argument because you have addressed it. It is the overall sense that you can't lose an argument as long as none of your opponent's statements go unchallenged, even if none of your challenges are substantial/meaningful/logical. It is the belief that if you can originate more threads of argument against your opponent than they can fend off, you have won, even if none of your arguments actually matters individually. I see Flowsheet Logic tendencies expressed all the time.
Notecard Logic is the tendency to treat evidence as binary. Either you have evidence to back up your assertion - even if that evidence takes the form of an article from [insert partisan rag] - or else you are just "making things up to defend your point of view". There is no concession to Bayesian updating, credibility, or degrees of belief in Notecard Logic. "Bob is a flobnostic. I can prove this because I can link you to an article that says it. So what if I can't explain what a flobnostic is." I see Notecard Logic tendencies expressed all the time.
Once you have developed a mental paintbrush handle for these tendencies, you may see them more as well. This awareness should allow you to discern more clearly whether you - or your interlocutor - or someone else entirely - is engaging in these practices. Hopefully this awareness paints a "negative space" of superior argumentation for you.