I still remember how I did not get jokes about inferiority of girls when we emigrated to Western Germany - I simply had never ever heard one before.
What speaks against your theory is that men died on all sides in WWII, but in the West (read: democratic societies), women's rights developed in a distinctively different/slower way.
PS: Yes, it was not all rosy, childcare was dual-use, it was also used for indoctrination of the youngest and even to some degree to control/check on the parents.
EDIT: It's probably revealing that my initial impulse is to consider this story as irrelevant because it focuses on the gender. Yes, after 26 years in the West I understand why it is relevant.