This argument assumes that the point of person A responding to person B is for person A to convince person B, specifically, at that specific moment in time of the specific details of their specific argument.
1) That's not how persuasion works.
2) It's not how ideas or the stubborn humans who hold them work.
3) The point is not, in fact, to convince that one particular person at that one particular moment in time. If that's your goal, then I might suggest that a phone call would be more appropriate. These are public arguments. Read by the public. They're useful far beyond the participants.
4) Minds change over time, rarely in the moment. If your standard for success is immediate agreement, then you've established an unrealistic (and misguided) goal. You'll never get that. But, again, that's OK, because that's not what you should be shooting for in the first place.
5) Argument is as much for you as it is for the person you're trying to convince. Working through objections is good for you. You impoverish yourself when you take this away.
6) People seem to think it's a really strong argument to point out that people get mad or emotional during debates, but I have no idea why I'm supposed to care. So a faceless, nameless avatar that I'll never meet showed too much emotion in an online debate? I have no idea why anybody thinks that's worth mentioning in any context. It's definitely not a persuasive argument for nuking all debate.
It's no wonder so many people have such a dim view of online argument, if your comment represents the conventional thinking on it (and it does).