What does it mean to be a man or a woman?

I think that the biological differences of man and woman extend to genitalia and slight differences in hormone and brain characteristics. However, I think that the hormone and brain discrepancies are a minor factor in our culture's gender hierarchy. Everyone's desire to fit into society creates a system in which women partake in their subordinate roles and men partake in their dominate roles. Many men and women want to fit in and live a socially accepted life.Obviously there are exceptions to this and simply do not want to follow these considered "norms". History has shaped gender to act a certain way.