This Seems Like a Fallacy

Yes, exactly, as the good doctor points out, social media is not the most elegant venue for invigorating debate. It is a wonderful medium for expressing one’s opinion while also revealing one’s blind ignorance and stubborn obduracy on a particular subject.

That said, we’ve all probably grown weary of the disagreeable Doctrinaire who argues for the sake of their belief and in the process of that defense purposely uses deflection, misunderstanding, and deception to avoid meaningful discussion or further exploration of the truth. In which case It is quite acceptable for one to say. QED, Quod Erat Demonstrandum, which can be a fancier way of saying, I’ve proved my point, or, I have fulfilled my responsibility, the rest is up to you. At that point we get into the ’pearls before swine’, or, ’playing Chess with pigeons’ phenomena. Communication is a two-way street. We all share the burden of knowledgable articulation and able apprehension. When one of these breaks down, well then, as the line from Cool Hand Luke goes, ”What we got here is a failure to communicate”.

The comment may be rude, inconsiderate, arrogant, dismissive, designed to end the discussion, but I don't see a fallacy and it may even be accurate, even if arrogant. It's possible the speaker may be asserting his expertise, by the way, arguing from authority, and that would be a fallacy, but I don't think you can conclude that just on the basis of his phrasing.

If the speaker means to end the discussion, you have to accept that, but if not, ask for clarification of some element of the previous argument, which may have some fallacy in it.

I agree with Michael on the fallacy. I would also point out that there is merit to the idea
“I am only responsible for what I say; not for what you understand.” Is one side actually failing to explain their position, or is the other side incapable of comprehending? It is usually a problem with the one doing the explaining, as good communicators know how to explain things so their audience can understand. A failure to get our audience to understand is more often than not, in my experience, an indicator that the one attempting to explain doesn't understand themselves what is trying to be explained.

Depends on how you read it or understand responsibility. In other words, the semantics are important.

From the point of view that a person's responsibility is limited to his own actions, and that the stupidity of the listener is his own responsibility, the statement is valid.

How far he can be responsible for the consequences of his actions is a different matter.

For example, if I say that Donald is a satanist empowered by Satan himself and should be shot with a silver bullet if anyone could manage it, and that shooting Satanists on a Friday is legal and is rewarded by the police with money.

Suppose Edward hears me and shoots Donald with a silver bullet, and in court blames me for what I said, then how guilty am I? Is it a defence to for me to say that I was speaking figuratively and never thought that anyone with a name like Edward could be so stupid, and in support for me to cite Wister: "When a man ain't got no ideas of his own, he'd ought to be kind o' careful who he borrows 'em from."

Again, does anyone have to be responsible in such cases? Whether the stupidity was mine for saying such a thing, or saying it to Edward, or Edward's for taking my saying seriously, how much stupidity can one be responsible for?

The question of the meaning of "responsibility" is not value-free; it is semantically bound. And who should act on it, if at all, is ethically open to question or argument.