Interestingly, one thing I've found that neither women nor men give up on is the idea of men as protectors. Even in cases where the woman is earning more, they'll often tell me that if there were a fire or something, they would expect the man to be the one to protect them.
Women have taken on traditionally masculine roles and professions, and there is no real equivalent for men. Men are still extremely reluctant, as we all are reluctant to see them, take on traditionally feminine roles or professions. That is just not something that they do easily.