This is difficult to pick apart. Can you say more? I could imagine, say, thinking of someone's contributions as assholeish introducing sentiment to the conversation in a way that cascades into making the whole thing even worse. In fact, I think I've seen that happen over and over again. I can imagine a framing of that as hyperstitional. 

It's nonspecific on purpose; a general factor of causes of "this conversation is making me mad". This could be caused by tone: concretely, an occasion where someone is trying to explain something, any topic, and using negatively charged words to describe people who hold my position, or just any other position, making my interlocutor sound smug. It can also be caused by a sense that the interlocutor isn't really engaging with my arguments, making me feel like I should be giving up on the conversation. Concretely, an occasion where I make a very extensive explanation of what I mean on some point, and the interlocutor completely denies acknowledging it, giving me no feedback on whether they even read it, or whether it addresses their concerns, choosing to instead focus on some tangential point. Bad, annoying discursive practice in general.

Both of these things can be "merely perceived" in some sense, but they almost always point to some kind of rhetorical dysfunction; either on the part of the speaker or listener. And one shouldn't assume their interlocutor is at fault; a thing that both the perceived asshole and the perceiver should understand.

If I had to dilute my point into a sentence, here, it's that being easy to talk to is a virtue, though only one among many, and this kind expression is often a sign that you aren't easy to talk to. This is of course very complicated, and has a ton of different factors going into it, but we ought to try.

You've given a plausible account of what might be happening in at least some cases that people use the rhetoric of "you'll never persuade anyone like that". I would like to give an alternate account--one that other posters have pointed to already, but that I'd like to highlight--and explore the possible consequences that adopting the strategy you've gestured at here, "going for the throat", might have.

When I say "you'll never persuade anyone like that", often what I'm feeling is something close to anger. I am "pissed off". Anger can be a sign of cognitive dissonance. If an argument makes you angry, you should try to explore the reasons for that anger; does it have to do with the contents of the message you're being passed, or the trappings, the way it's expressed? Does it have more to do with the context--were you intending to not talk about this, is it an inappropriate context for the discussion, are you avoiding something...

When I examine these feelings in that context, there is often a common link between them: my interlocutor is being a huge asshole. That is: I'm saying "okay, smartass, see how this rhetorical style works out for you". I am often forcefully trying to get them to either stop or change their tone.

Perceptions that someone is "an asshole" may well be affected by cognitive bias; no one could reasonably deny that questions of affect aren't to a great extent, in many people, mediated by the halo effect, by the speaker and listener's perceived alignments, by irrelevant trappings. But it is possible to be an asshole. It is possible to be an asshole even without intending it. Indeed, there are ways and magnitudes to what is perceived assholehood, but I will give a brief theory of what it means to be an asshole here: being an asshole is being more forceful, rude, or otherwise contentious than is necessary to communicate a point.

I think that your theory--and especially the "this is what your interlocutor really means" framing you've used, is likely to lead to precisely the opposite of the appropriate response to this kind of feedback. That is, it's likely to lead to doubling down when slowing down would have been the appropriate response. I advise anyone reading this post to take that heavily into consideration.