The "you are mean because I am a girl" mentality translates, for me, as a "you are mean because you are a boy" which, really, is just as sexist as, and no better than a man going "I can pay you less because you are a woman".

Not really, because a woman going "you are mean because you are a boy" is, at the very worst, an isolated action, whereas "I can pay you less because you are a woman" ties into a larger social context.