A few thoughts about hitting girls

I was watching "Daddy's Home" a while ago, and in one scene, both the step dad and real dad are trying to teach the son how to defend himself against a 4th grade bully.  A little farther along into the movie, it is revealed that the bully is actually a girl.  Then everyone gets all up in arms over hitting a girl.  Now, I'm a girl, and it is a little surprising to me that I actually think this way.  My question is, why is it not ok to hit a girl if they're the ones throwing punches first?  It's been passed down through generations that it is never ok to hit a girl.  Boys, yes throw down.  But girls have always been a different story.  It came around (I assume) when girls were universally believed to be the weaker sex and couldn't really fend for themselves, and they needed a man to take care of them.  So at that time, yes I get why.  But now?  Not so much.  Women have made huge strides in becoming equal to men, and there are so groups out there to make women equal to men in every way.  But this seems to be one thing that no woman has ever come forward and really said "you know what, it's ok to hit a woman.  If she's being a bitch and deserves it, then throw down."  I don't feel that women should really pick and choose on what issues they're equal to men.  It should be an all or nothing deal.  But then again, maybe something like that will always be just a thought, and nothing more.