Here are reasons Paul gives why every woman should wear a head covering in the church services:
1. Because of the headship of man (vs 3-6)
1 Corinthians 11:3 But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.
--The Scripture clearly teaches a principle of headship, whether we want to believe it or not. The head of the woman is the man. The woman ought to keep her head covered for that reason alone. If she doesn't it is to her shame.
1 Corinthians 11:6 For if a woman is not veiled, let her also be shorn: but if it is a shame to a woman to be shorn or shaven, let her be veiled.
2. Because of God's order in creation (vs 8.9)
1 Corinthians 11:8-9 For the man is not of the woman; but the woman of the man: for neither was the man created for the woman; but the woman for the man:
--It is also a symbol of order. The man first, the woman second.
3. Because of the angels (v 10)
1 Corinthians 11:10 for this cause ought the woman to have a sign of authority on her head, because of the angels.
--We don't have to understand the reason; we must accept it by faith. But the Lord says it is because of the angels. In other Scriptures it says that the angels desire to look into the salvation of man. They have not been redeemed. They don't understand it.
4. Because of a sense of propriety (v 13)
1 Corinthians 11:13 Judge ye in yourselves: is it seemly that a woman pray unto God unveiled?
--It is just the proper thing to do. That is what Paul is saying here. It is a rhetorical question that doesn't require an answer. It is just the proper thing to do. You shouldn't have to be told this.
5. Because of the natural order of things (the distinction between male & female and the woman's natural covering; vs 14,15)
1 Corinthians 11:14-15 Doth not even nature itself teach you, that, if a man have long hair, it is a dishonor to him?
15 But if a woman have long hair, it is a glory to her: for her hair is given her for a covering.
--Nature teaches you this. In almost all cultures women have long hair, not men.
It is a shame for a man to have long hair. This is true in almost every culture. Nature teaches it. It is the natural order of things. It is very beautiful to see long hair on a woman.
6. Because of the practice of all the churches (v 16)
1 Corinthians 11:16 But if any man seemeth to be contentious, we have no such custom, neither the churches of God.
--This is Paul's strongest argument yet. If you are contentious about this doctrine, don't stay here. You are not welcome. We have no such custom of being contentious. Neither do the churches of God have any custom of being contentious. The churches of God obey this command, this ordinance (verse 2), that I have given to them. If you are not going to accept it; then there is no place for you here.
Romans 16:17 Now I beseech you, brethren, mark them which cause divisions and offences contrary to the doctrine which ye have learned; and avoid them.