I'm not saying teach people that they need someone. I am saying that often we do need someone- not to fill in the gaps, but to give us someone to share with. There is nothing wrong with doing life solo, but there's also an advantage to being with someone that you trust and count on like no other. We (as we typically do in America), swung the pendulum widely, rather than moderating and improving the lot of women. We used to tell them they needed a man to survive. Now we tell them that they don't need anyone at all, and it's led to a sort of self-absorbed view in general.
As for need- yes, I think it goes both ways. Men and women need each other- not because either is inferior, but just because it adds a really nice dimension to life to have someone you can trust and relate to completely. I was married for a long time. I am fine without a husband, and I can support myself without any problems. That being said, I miss having intimacy (psychological as well as physical). It's not that I NEED a man. It is that I enjoy having that type of relationship.
I am independent and assertive regardless of my relationship status. When I was married, my husband told me on more than one occasion that one of the things he loved about me was that I was not afraid to stand up to him. He was a highly intelligent man, with a mind of his own, and had I been passive, I would have been completely irrelevant. That is not a healthy relationship. I don't advocate for people to marry their opposite, due to some need to fill in their own blanks, but for people to form relationships which challenge them to grow and improve as humans.