no, it's a rejection of your argument from authority, not a supporting claim of "overreaction from people who aren’t used to pushback". if you think there are other substantial coutnerclaims, please make them.
You said: “the people telling you they're being silenced is a group of privileged folks unaccustomed to being pushed back upon publicly, with "cancel culture" as the reactive appellation for that push back?”
Which I interpreted as: “the only people who complain about cancel culture are unaccustomed to pushback” and disproved by counterexample.
It occurs to me now that perhaps you didn’t mean “all”. You meant “some”. That’s called nutpicking and it means your original claim wasn’t substantial enough to discuss in the first place.