Note 11 at 1 Cor. 11:11: Paul is not teaching some tyrannical system of the man having lordship over the woman. He is just stating that in the marriage relationship, the Lord has given the husband the greater authority. This is really no different than different levels of authority in the work place or a game of sports, etc. Any time two or more people endeavor to do something, there has to be someone in charge to do things efficiently. The husband is in charge.

But Paul makes it clear in verses 11-12 that the woman is not just a second class citizen. The man wouldn't exist without the woman. Peter said in 1 Peter 3:7 that the husband needed to give honor unto the wife, as the weaker vessel, and as being heirs together of the grace of life; that your prayers be not hindered.

Marriage is actually a partnership. Paul, when speaking about marriage in Ephesians 5:21, said we were to submit ourselves one to another. But when an impasse arises, the Lord has given the greater authority to the husband.