I don't think you were wrong to get mad in either case. It's a natural response to being insulted or hurt.

The solution is to become so secure in who you are that it doesn't matter what other people say. If you're not a "dyke," they're wrong and it makes them dumb and imperceptive. If you are, you have no reason to be mad, because it's not a bad thing and it's something you like about yourself.