This doesn't mean that the user hates womankind, just that they are expressing disdain for a certain woman.
Listen up Captain Clueless, when someone uses a word for a woman's genitalia to insult a certain woman, they're definitely not doing it because they think woman as a group are wonderful people. It's like when straight people say "I don't care if you're gay, just don't be a faggot!", or when white people say "I don't care that you're black, just don't be a nigger.". Whatever their justifications, it's obvious that this person is not your friend, they imagine themselves above you, able to judge you as a representative of your group, and will move against you or hurt you if they think they can get away with it. A woman/gay person/black person that agrees with this line of thought ("don't be a "), has internalized a lot of self-hatred.
Do you get all huffy when somebody calls a guy a dick?
Yes I do. Like I said, using gendered insults says a lot more about the person using them than the person being insulted.