I see where your coming from but...

... to me you are going to far in the opposite direction. If women ruled everything it wouldn't become too much better if it became better at all.

The problem is sexism. Both against women AND men. Parents won't let their kids where what they want, or play with what they want. Little Jimmy wants to try on a tutu? GOD FORBID! Little Suzy likes dinosaurs and trucks? GET HER A BARBIE! Men and women both promote these gender specific ideals. Not only this but if parents try to raise their kid in a somewhat gender neutral way (ignoring gender is also ridiculous imo and complete gender neutrality is just as silly to me) school will then enforce the stereotypes.

My kids won't be forced to go to school though and I will let them where and play with what they want. EVEN THEN they will be living in our society and they are still going to pick up on stereotypes... but with open minded parents and no forced schooling they will be able to make their own decisions.