1 Corinthians 11:7-10 (NIV)
A man ought not to cover his head, since he is the image and glory of God; but the woman is the glory of man. For man did not come from woman, but woman from man; neither was man created for woman, but woman for man. For this reason, and because of the angels, the woman ought to have a sign of authority on her head.
Paul makes an argument here, appealing to the order of creation, that man is the head of the woman. This is not a popular verse. It ruffles some feathers. But it is the word of God for us. Why is it important? No one would argue with the idea that their should be a hierarchal order of authority in any organization from government to companies. Then why bristle when the same thing is applied to the family organization?
When someone has rank over another, value and worth and ability are not what are being compared. It is simply a necessary organization to enable a group to function as a unit by eliminating confusion. Christ is subordinate to the Father, yet they are equal. In a earlier verse, Paul even says that the head of Christ is God. We see all through the gospels how Jesus subordinated every thing he said and did to the authority and direction of the Father. And yet, He is co-equal and now glorified with the Father.
By going back to the original creation of Adam and Eve, Paul puts to rest any other argument against this idea. What a curious phrase, "because of the angels." Paul does not elaborate as if we should know what he means by this. What we can know is that it is given as a reason why the order of authority should be observed. The angels were observers during the creation; they observe us today. A fallen angel can never be redeemed, so for them, the redemption of man is something to marvel at. They know submission and authority better than any other creature. For man, who has the incredible privilege of redemption, to usurp the God ordained order of authority is simply appalling to an angel.
The head covering business is like stripes on a soldiers uniform indicating rank. Paul calls it a "sign of authority." Just like the army wears different uniforms today than they did 2000 years ago, so too men and women in their family relationships have a different practice. But that is not the point.