I recently posted some scripture about women having long hair and I was asked in a pm to justify and expand on the context of that verse. I am doing it here because that thread was about DD, not theology. Please feel free here to have a thorough discussion of 1 Corinthians 11:2-15.
First, I want to say that the context of this passage is not a personal appearance. It's about procedures for prayer and prophesy. The comment about hair is not the main point, it is a comment made to explain the main point. However, it does reveal what is in the mind of the author (Paul and the Holy Spirit) about hair.
Here is the scripture:
v3 starts with "but" telling us that what is to follow is not one of the ordinances (commands) referred to in v2. The main point of this passage is an instruction from Paul in his apostolic authority and under divine inspiration but not previously given by Christ.. (2) Now I praise you, brethren, that ye remember me in all things, and keep the ordinances, as I delivered [them] to you. (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. (4) Every man praying or prophesying, having [his] head covered, dishonoureth his head. (5) But every woman that prayeth or prophesieth with [her] head uncovered dishonoureth her head: for that is even all one as if she were shaven. (6) For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered. (7) For a man indeed ought not to cover [his] head, forasmuch as he is the image and glory of God: but the woman is the glory of the man. (8) For the man is not of the woman; but the woman of the man. (9) Neither was the man created for the woman; but the woman for the man. (10) For this cause ought the woman to have power on [her] head because of the angels. (11) Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord. (12) For as the woman [is] of the man, even so [is] the man also by the woman; but all things of God.
. (13) Judge in yourselves: is it comely that a woman pray unto God uncovered? (14) Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him? (15) But if a woman have long hair, it is a glory to her: for [her] hair is given her for a covering.
-- 1 Corinthians 11:2-15 KJV
The reason for this instruction is not fully explained, v10 gives it as "because of the angels." Much debate and many sermons have tried to explain that phrase, but I am convinced that we just don't know for sure why it would matter to the angels. What is clear to me is that this instruction is not culturally dependant, whatever is going on with angels isn't specific to 1st century Corinth.
v4-5 include the main point. Men should pray and prophesy with no head covering while women should do so with a covering.
v6 says that if a woman is going to prey or prophesy without a head covering then she might as well cut her hair.
v7-10 seeks to explain the reasoning for the difference between men and women. This seems to relate somehow to the principle of submission or marital roles, but it's a bit vague as a full explanation.
v11-12 are a parenthetical statement making sure that the reader knows that the author is still upholding the equal value of men and women in Christ.
v13-15 try to back up the previous point by appealing to facts that the reader already believes. One of those facts is "if a woman have long hair, it is a glory to her: for her hair is given her for a covering." Glory here is the antonym of shame.
v16+ deal with another topic entirely, that topic is contentiousness within the Body of Christ
So, in conclusion, neither God nor Paul is commanding that women must have long hair. They are saying that it is her glory to do so. They are doing so as a side comment in a discussion mostly about the use of head coverings during prayer and prophesy.