Being mean isn't the same as the ad hominem fallacy

I had an argument on the internet a while ago. In fact, I've had dozens of arguments on the internet. Usually, the arguments I get into relate to things in which I have an emotional investment, so occasionally, I indulge in pointing out that arguing the contrary point, because you think it's fun, makes you an asshole. I want to explain, now, why that's not committing an informal fallacy.

An ad hominem attack is when you attempt to persuade others that someone else's claim must be false, because they posses damning character flaws. Here's an example of an ad hominem argument:

Person A, who's wearing a peach tank top and listening to a playlist of Blink-182 and the Pixies: I think X is true.

Person B, who has a strong personal investment of the audience believing X is false: Well, you obviously can't be trusted because nobody who wears that kind of shirt and listens to those bands is worth listening to.

Large segments of the internet, however, seem to have become persuaded that an ad hominem attack is just any argument at all in which one's feelings get hurt.

In all of these examples, person B is not employing an ad hominem attack:

Person A: I think X is true.

Person B: I disagree. Here are reasons why. Also, you're an ass face.

Person A: Calling me an ass face is ad hominem.

Person A: I think X is true.

Person B: You have been being rude to me during this conversation, so I'm no longer interested in engaging with you.

Person A: You can't call me rude! That's an ad hominem attack, and it means you're wrong.

Person A: I think X is true.

Person B: Fuck off.

Person A: That's not fair -- you have to be nice to me, we're having an argument. It's ad hominem.

Person A: I think X is true.

Person B: X is not true. Here are reasons why. Defending X is, in fact, directly harmful to groups Y, Z and F. Here are explanations why. In my estimation, your persistence in defending X makes you an asshole.

Person A: Ha! You used a bad word! That means I win. Ad hominem!

In fact, in these cases, person A is engaging in the ad hominem fallacy -- they're attempting to undermine B's position, or bolster their own position, by framing B's expression of frustration, their desire to leave the conversation, or even the actual, defended position of their argument as being an attack on A's credibility.

I'll probably be linking people to this in the future, so here's a PSA for anyone who's here because we're arguing and you're trying to call me out on something I'm not doing:

MESSAGE TO PEOPLE I'M ARGUING WITH: the informal fallacies aren't a system of rules by which you can win an argument on a technicality. They're a vocabulary with which other people can discuss the merits of our conversation.

If you think I'm not playing fair, feel free to tell me where my argument is flawed. If you feel personally hurt by my position, understand that it's entirely valid for my position to be that you're a bad person, and I don't care if that makes you uncomfortable.

And if you think that a sarcastic, dismissive, or angry tone is a reason that you don't have to pay attention to the content of a conversation, then you should think hard about whether your goal is to defend challenges to your ideas, or to collect a bunch of effort tokens that you can show off when folks accuse you of not considering the opposing view.

You're allowed to walk away from a conversation that's making you upset. I'm sure as hell not going to keep trying to engage with you if you ask me to stop.

But if you walk away from a conversation and tell people that you were right because I was mean, you're committing the ad hominem fallacy.

And you're an asshole.