Does the Bible teach men and women are almost equal in the union yet the man is still the head?

Les explains that the man and woman come together in a union that puts them almost on an equal basis, but the man remains the head of the union. The man came from God in creation. Paul does not want the Corinthians browbeaten or driven into rebellion, so he tempers his correction, yet he insists things must be straightened up. Everything done in the local church must be done in order, not in a mass of confusion, because God is a God of order. He also asks them to judge what is comely, notes that nature teaches long hair is a shame to a man, and says a woman's long hair is a glory and a covering to her.