Saying that an argument is fallacious isn’t the same thing as saying that because the argument is fallacious, it is therefore wrong. Surely you don’t think tha

Saying that an argument is fallacious isn’t the same thing as saying that because the argument is fallacious, it is therefore wrong. Surely you don’t think that all cases of pointing out that something is a fallacy need to include a disclaimer saying “but of course, that doesn’t in itself imply that the conclusion is wrong”. After all, you did not include such a disclaimer yourself. That being said, it seems that the back and forth here doesn’t really seem to have any statements of the form “X (and also Y), therefore Z”. So, I guess that makes it hard to analyze formally as an argument, as instead much of the things like that being explicitly said, there are things being mentioned, with a number of things left implicit.