Now I commend you because you remember me in everything and maintain the traditions even as I delivered them to you. But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God. Every man who prays or prophesies with his head covered dishonors his head, but every wife who prays or prophesies with her head uncovered dishonors her head, since it is the same as if her head were shaven. For if a wife will not cover her head, then she should cut her hair short. But since it is disgraceful for a wife to cut off her hair or shave her head, let her cover her head. For a man ought not to cover his head, since he is the image and glory of God, but woman is the glory of man. For man was not made from woman, but woman from man. Neither was man created for woman, but woman for man. That is why a wife ought to have a symbol of authority on her head, because of the angels. Nevertheless, in the Lord woman is not independent of man nor man of woman; for as woman was made from man, so man is now born of woman. And all things are from God. Judge for yourselves: is it proper for a wife to pray to God with her head uncovered? Does not nature itself teach you that if a man wears long hair it is a disgrace for him, but if a woman has long hair, it is her glory? For her hair is given to her for a covering. If anyone is inclined to be contentious, we have no such practice, nor do the churches of God. (1 Corinthians 11:2-16, ESV)
In my travels through presbyterian and reformed Churches, the question almost everyone asks about this text is, "Should women wear head coverings in worship?" Of course, this is the entirely wrong question to ask about one of the Bible's most important texts for gender relationships. (I'm not kidding: I put it right up there with Genesis 1, 2 and 3.) Since you asked so nicely, I'll explain why it's the wrong question.
An opening note: it's not clear whether the "head covering" in 1 Corinthians 11:2-16 is the woman's hair, a piece of cloth, or some other type of headgear (such as a lovely
Easter bonnet, about which I could write a sonnet). It's even less clear whether this injunction applies to all women or only those of the married variety. These issues get even murkier in the original Greek (which is the case more often than you may think). However, that's not really much of a problem in practice, as we shall see.
Paul tells us the woman is to cover her hair while praying and prophesying, which are both speech acts. This is peculiar because later in the same letter he tells us that women are to remain silent in the Churches (1 Corinthians 14:33-34). Here we have a conundrum: why would the Apostle tell women how they should dress when they are doing something he has barred them from doing? Not to put too fine a point on it, he might as well require men to wear neckties when visiting bordellos.
In the broader context of 1 Corinthians, Paul identifies prophecy as a speech act directly inspired by the Holy Spirit, without any mediation by the speaker him/herself: that is, the speaker opens her/his mouth and out come the Spirit's (not his/her) words (1 Corinthians 14:1-5). The Spirit may also give prayer in this manner (1 Corinthians 14:14-17). Thus, when he joins "praying and prophesying" (1 Corinthians 11:4-5), he has in mind these sorts of unmediated, Spirit-gifted speech acts.
These were different in nature from the teaching (learning's necessary companion) Paul has in mind in 1 Corinthians 14:33-34. Teaching is the result of study and preparation: while Christian teaching assumes the Spirit's illumination of the Bible, the teacher's words are chosen and formulated into speech by the teacher her/himself. Paul can forbid women to teach at the same time he expects the Spirit to speak through them because the two speech acts are very different in origin and performance.
This means that the head covering regulations Paul sets out in 1 Corinthians 11 apply only in worship contexts in which one expects the Holy Spirit to start speaking through male and female Christians without warning or preparation. Since we live in a time during which the Spirit does not act in this way, we (and by "we," I really mean "Christian women") don't need to ask, "Should women wear head coverings in worship?" The point is moot.
[The above argument assumes the
cessationist view of confessional presbyterianism. For brevity's sake, I will not attempt to defend that position here. I realize this may limit my audience to presbyterians, but I can live with that.]
It seems to me there's a hermeneutical problem which has led many to miss the obvious point that 1 Corinthians 11's discussion of head coverings is irrelevant to the contemporary Church: we often go to the Bible to find rules. For the serious Christian, it's awfully difficult to find a rule in the New Testament and not attempt to implement it. In this case, that rules-oriented hermeneutic (philosophy of interpretation) has led many to miss Paul's much more interesting teaching on gender relations and the questions it raises.