Originally Posted by Ponyboy
Well, violence against women is probably not something that Batman cares too much for. In the heat of the moment he may have been shocked by the fact that he hit her (not something he would normally do)... and maybe he thought she was attacking him because she felt threatened by him. I don't think Catwoman was clearly a "villain" yet to him at that point in the film.
Still not buying it.
Yes, Batman is against violence towards everyone (not just women), but that does not apply to people who are trying to hurt others (including himself. Batman is a smart fighter, and what Catwoman did (after she drew first blood) was rather obvious, considering she was definitely trying to hurt him. It's the kind of obvious ploy that only stupid people will fall for, and Batman is not that stupid.