You're a victim of the biases and presumptions of your own egalitarian culture.

There is a basis. Men and women are different and sexually complementary. One obvious reason is that the sexual tension and constant presence of people of the opposite sex (female orders exclude men also) and subsequent temptation and stirred concupiscence can be a distraction to the spiritual life. But the tendency for sex segregation occurs naturally. People tend to befriend people of their own sex because of an affinity of similarity, not complementarity. This is an important distinction.