Lot of words to describe cherry-picking, but… yeah. All of that is true.
Not even a vegan. I love meat. But the classic image of the vegan that constantly reminds you of the fact is not at all consistent with my experience with the several in my life…
You’re describing the Fallacy Fallacy, being that the implication that the argument is necessarily wrong because a fallacy has been committed. That a fallacy has been committed by the other party should not alone be used as an argument against the point itself.
I.e. you committed a strawman fallacy by stating that all strawmen are made of straw, therefore no strawmen are made of straw