If I had to pick one response philosophers give that bothers me more than any other, it's when you criticize philosophy and philosophers get all snarky:
Criticism of philosophy is philosophy! So you're just doing philosophy!
People who are criticizing "philosophy" probably don't intend to criticize any and all systematic thinking about abstract issues. Rather, if we're being charitable (something one would think *philosophers* of all people would champion), they may appreciate that critics are probably just criticizing philosophy as an academic field or subculture, or are criticizing specific features of philosophy-as-it-is-practiced-by-philosophers, e.g., conceptual analysis, obsessive focus on language, questionable ways of employing intuitions, and so on.
I’m also not saying there aren’t ill-informed criticisms of philosophy that are critical of all philosophizing, or criticize it for very stupid and ill-informed reasons. However, the problem with these objections isn’t that they’re “doing philosophy,” but that they’re critical for bad reasons or are ill-informed.
But philosophers often lump all criticism into this category. One would have thought philosophers would tend to be more charitable, do their best to understand where critics are coming from, and offer a substantive response. Instead, they often reach for the lowest shelf: a snarky "that's self-defeating" objection that is lazy and ironically exemplifies exactly what so many critics hate about how many philosophers practice their craft to begin with.
More generally, self-defeat or performative-contradiction style objections are often quite terrible: they often rely on presumptions that a critic is free to simply reject. Unfortunately, many philosophers seem to favor style over substance, and to try to go for a quick kill with something rhetorically clever.
The prevalence of these sorts of snarky responses, often dressed up in the formal attire of syllogisms and formal names, comports with my worry that much of philosophy functions, in practice, as a sort of intellectual game, rather than a serious approach to solving problems.
You really think "I'm free to reject a premise" (whatever that means) shows self-defeat arguments are "quite terrible"? As if "I'm free to reject a premise" shows an argument is "quite terrible".
I also noticed you never actually tried charitably constructing the objection. Just went with an uncharitable reading that's easy to knock down & called it a day, only after dropping emotional buzzwords "it's snarky!" & (ironically) calling it uncharitable.
So maybe you could actually try understanding where objectors are coming from instead of cringely emoting "snarky tho"? (facepalm)
For those who actually care to properly interpret the objection, competent proponents (Joe Schmid & Michael Huemer), as opposed to beginner no-name randos, design the point against a very specific view. (See Schmid's video "Is philosophy useless?" 1:29)
They (correctly) point out that the view (held & defended in academia) that philosophy doesn't produce knowledge implies any defense of such a view wouldn't make you know the view's true, as such a defense would be doing philosophy.
It's very basic. And may not apply to the view you hold FYI.
Finally, you strike me as a philosophy-basher who's heavy on vague platitudes "philosophy functions as an intellectual game rather than a serious approach to solving problems" & lacking on empirics for your crazy grand claims "many philosophers favor style over substance" (no data provided).