As a mother of a young boy, I have chosen not to teach my son "Don't hit girls". Our rule is don't hit, unless it is unavoidable, for example in tai quan doh class or to defend yourself.
My reason for this is to help him understand that hitting a girl is just as likely to get him hit back as hitting a boy and that hitting a boy, girl, animal, etc. is just not an acceptable way to solve a problem or vent frustration. Moreover, I do not wish him to start out seeing women as possible victims in need of protection or deferential treatment based solely on sex/gender.
On the other side is the 'ladylike' ideal for girls. One example is: "He did it because he likes you", a phrase I much resented as a child. In my case that was the response of the playground person when a boy kept pushing me. When he did not stop after repeated requests and the adult would not help, I finally yelled "No" and pushed him down. He did not like me enough to try again after that.
I'm curious to hear how others navigate the sex/gender minefields.