If an argument is upsetting or frustrating me then I will stop replying. I like to argue for fun and as soon as it's not fun I try to disengage because there is already enough angry people on the internet and I don't want to be another one.
If it's an unfair ban, I'll post one comment saying it's unfair and possibly insulting the mods. Only one comment otherwise it turns into a fight and I get banned to.
The reason why I don't really get upset by internet arguments is because I remind myself that we don't know each other and never will. We both have completely different world views and perspective and that's fine. I've also been on the internet a long time and learned the hard way that arguments on the internet are a pointless waste of time if your goal is to get the other person to change their mind.
You also never know how serious another person is. I once strung a youtube comment section argument out for 8 months. My position was that space was not real and this guy was an idiot for believing the footage was real. Of course I believe space is real its just funny to say its not and watch people lose their minds.