look, it’s a word most american women don’t hear directed at themselves outside of really hateful or abusive contexts. i have been called “bitch” in the grocery store. i was called “cunt” by my abuser, and only by him.
the person who challenged you has a good point - the use of that word in american culture is intended to be particularly dehumanizing and degrading to women.
compare - if you had used “n…” you would have likely been challenged there as well, regardless of your intent in using that word or your own identity.