Hans Hansen has a good discussion of fallacies at the SEP. One of the sections discusses what Hansen calls the 'appearance condition', namely, that to be a fallacy an argumentative error must have a semblance of correctness. This is one of the fundamental ideas of fallacy theory, going back to Aristotle himself, but it has received some pushback more recently as being too psychological. Hansen notes that two reasons to keep it:
(1) "It can be part of explanations of why reasonable people make mistakes in arguments or argumentation: it may be due in part to an argument’s appearing to be better than it really is."
(2) "The appearance condition also serves to divide mistakes into those that are trivial or the result of carelessness for which there is no cure other than paying better attention, and those which we need to learn to detect through increased knowledge of their seductive nature."
But these are both 'psychological' in the sense the critics mean, important as they in fact are. There are other reasons why the appearance condition is important, and at least one of these is, I think, a more direct answer to the claim that the appearance condition is too much a matter of psychology and subjective appearance: namely, that it is not psychological at all. Discussions of the mask of the sophism or the misleading character of the argument have rarely been conducted in terms focusing on psychological states. Rather, the appearance condition is concerned with the relation the fallacy has to other arguments.
This can be of importance in several ways. For instance, a common way of thinking about fallacies is to suggest that they are argument forms, or things purporting to be argument forms, that fall short of a standard of correctness. All well and good, but there are endlessly many standards of correctness one might have in reasoning. Even formal fallacies don't all answer to one standard, since (for instance) formal fallacies for a propositional logic are not necessarily the same as formal fallacies for a term logic. It's one of the first lessons anyone gets in validity that an argument may be invalid in one way and yet still be valid according to a more appropriate way of determining validity. We usually just check which standard of correctness to use by looking at which common standard would make the argument a good one -- but fallacies aren't made good arguments, or they wouldn't be fallacies. So how do we determine which standard of correctness is most appropriate for understanding the fallacy itself? By the relation of the fallacies to arguments that are correct under various standards. And, indeed, how does anyone actually study fallacies? By comparing them to good arguments. To be recognizable as a fallacy, the fallacy must be 'groupable' with good arguments in some way.
The appearance condition is thus a classification requirement, and it simply tells us, in practical terms, that we should understand fallacies by determining the relation of the fallacy to arguments that are good and correct. Analyzing an error requires recognizing what it falls short of; and that by its nature is equivalent to identifying what standard to which it 'appears', but fails, to conform. Conceivably this could involve some kind of psychological approach, but when one recognizes that the formal fallacy of denying the antecedent has the 'appearance of correctness' of being grouped with modus tollens and modus ponens, this is not a psychological matter at all: one can identify precisely the purely logical features involved. Thus the objection goes astray from the beginning.