You might want to review 1 Cor 11, and I will quote it in full further down the page.
Tremendous thanks are due to Katherine Bushnell for her book, God's Word To Women. Much of the meat of this post and certainly its key point are a mere retelling of her analysis of 1 Cor 11.
1 Corinthians 11 is the sole chapter of the bible that discusses women and veils. 1 Sam 15:30 talks about David covering his head while ascending Mount Olive in a state of mourning. The Greek word for cover, as used here, appears three times in the New Testament - all in this chapter. The word covering, as used here, appears one other time in Hebrews and refers to the heavens that God will fold up and change. Nave's Topical Bible references wimples worn by wanton daughters of Zion, Rebekah wearing a veil when meeting Isaac (a custom of her homeland, not Isaac's), and Tamar imitating a harlot to gain a child by Judah who had betrayed her. Not a whisper about women veiling in prayer. There's nothing in the bible on this topic.
Well, there is 2 Cor 3:13-18. Paul, shortly after writing 1 Cor 11, wrote 2 Cor 3, which ends But we all, with open face beholding as in a glass the glory of the Lord, are changed into the same image from glory to glory, even as by the Spirit of the Lord. Paul carefully explains how the physical veil kept Israel from seeing the whole law on Moses' face, and how the spiritual veil kept them from understanding the truths they heard.
So, we are dealing with another scriptural island. We have no other scriptures that confirm the standard interpretation of 1 Cor 11.
And the standard interpretation of 1 Cor 11 has more than a couple of holes! Let me address one immediately out of sheer disgust.
For this cause ought the woman to have power on her head because of the angels.
The standard interpretation of this verse, that fetching women will tempt their angels, is offensive to all parties. It's offensive in it's ludicrousness most of all. Human women do not tempt neuter angels, and if they did, they would have plenty of opportunity to do so while doing other things than prophecying and praying. Would these interpreters have women fear to pray without a clothing check first? Should women fear their own ministering spirits? If there were any weight to this slur, it would collapse on its own. What, do women become invisible to angels when they have veils on? Or just unattractive?
Look, I know that someone is going to have to bring up the Nephilim, etc. Just know that the men who came up with the unbecoming theory about the "sons of God" in Genesis are the same men who say charming little things like, "I would sooner feed the scripture to my dog than let a woman read it." This verse as written contains no such implication of lust. Why add it?
Back to the subject.
1 Cor 11 is an island in the scripture, so we must use internal methods of interpreting it. It seems to say things that are opposite to the rest of scripture, namely that women should veil when praying. Paul himself says a short time later that we all come to God with open faces. Given these external conflicts, we might expect to see some internal contradictions. And we do.
Does nature teach you that long hair is a shame to a man? It doesn't teach me that. I played in an all spanish speaking soccer league, and there was nothing unmanly about some of the manes those men sported. Certainly not to the women who flocked to them. Does the lion teach us that long hair is a shame to the male? The peacock? The question makes no sense.
Paul seems to give us a straight hierarchy of headship in verse 3. Then he says that a man covering himself before his Head is a shame, and a woman uncovering herself before her head is a shame. What sense does that make?
Paul goes to a lot of bother to seemingly show that the woman is under the man in verses 2-9, then reverses himself in verses 11 and 12. I will grant you before you make the argument that you can finagle the verses to kind of mean something, but Paul is not known for contradicting himself this confusingly.
And he finishes the whole passage by saying that his churches have no such custom. Why not just accept at face value that Paul is saying Corinth is the only place on earth that is trying to veil their women. That's the plain meaning of the verse, but the standard interpretation will have none of that. What then do they say Paul means? That the churches have no custom of being contentious? That's a falsehood on the surface. ;-) But, even if we try to make that meaning work, it doesn't. Who would say that his church didn't have a custom of being contentious?
Somebody is working really, really hard to make this chapter say what he thinks it says.
The Chief Clue to Clearing up 1 Corinthians 11
Every man praying or prophesying, having his head covered, dishonoureth his head.
It is all very simple if the problem is exactly what is stated in verse 4. Men are covering their heads. Women are imitating the men. Paul does not consider either the actions of the men or the women to be right, but neither is he willing to declare them anathema.
Verse by Verse
1 Be ye followers of me, even as I also [am] of Christ.
This verse belongs at the end of chapter 10, not at the beginning of 11. I wonder how mistakes like this get propagated over the centuries? Note that even the translators place a paragraph mark at the second verse.
2 ¶ Now I praise you, brethren, that ye remember me in all things, and keep the ordinances, as I delivered [them] to you.
Paul does not begin with a rebuke, but praise.
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.
"Head" in Greek can as easily mean "fountainhead" as "hierarchical head." For reasons found below, I will accept the fountainhead meaning. Either way, the verse does not remove Christ from the woman. The man is another fountainhead for the woman, but Christ will always be her Head.
4 Every man praying or prophesying, having [his] head covered, dishonoureth his head.
Jewish men wear a covering called a Tallith in prayer. This covering is not a veil, but it conforms to the meaning of the Greek word for "covering" admirably. When a Jewish man dons the Tallith today, wikipedia reports that he speaks the following blessing.
Blessed are You, Lord, our God, King of the universe, Who has sanctified us with His commandments, and commanded us regarding the commandment of fringes
May it be the will before you, Lord, my God and the God of my forefathers, that it should be considered the commandment of fringes before You as if I had fulfilled it in all its aspects, its details and its intentions, as well as the 613 commandments that are dependent on it. So be it, [consider what we have said].
So, the tallith is a testimony to a dead law. Well might Paul say that when a man dons the covering, he dishonours his Head - Jesus Christ - Who took away that law that was set against us. That man binds back to himself those dead ordinances Christ died to loose.
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.
We will search in vain to find anywhere in scripture that urges a woman be shorn. We find her head being uncovered by the priest in Numbers, during the administration of the water of jealousy, but it would be a stretch to assume this to be Paul's point of reference for verse 6. Paul is here referencing an Oral Law of the Jews. The commentaries pretty uniformly either accept or at least do not reject this view.
Given that point, Paul is here explaining that the shame that the woman brings upon her head is shame brought upon her husband. If a Jewish wife appears in public uncovered, Jews outside the church might call for her husband to divorce her. This would be a shame upon her husband.
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.
Paul here quotes the oral law, then makes a concession to it. The word, "but," here carries the sense of "therefore." This law exists, therefore if you are a Jewish man, and since Jewish oral law would require you to acknowledge your wife as disgraced if she went unveiled, then I permit her to be covered.
Paul tells the man he must not shame Christ with a covering, but the woman he permits to be covered even before her God for the sake of a disgrace she might bring on her husband before men.
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.
Do you see how the contradictions of the standard interpretation melt away? A man should not cover his head because he steals from the glory of the Lord Who bought him with a great price. The woman, however, might shame her Jewish husband should she break this oral law of the Jews. The woman is the image and glory of God as much as is the man - namely in as far as she is in Christ, Who is the only true Image of God. But the woman is also the glory of her husband.
8 For the man is not of the woman; but the woman of the man.
Therefore, a wife is allowed to support her husband in this matter. Paul makes it a matter of liberty for her.
9 Neither was the man created for the woman; but the woman for the man.
So Paul concludes his arguments freeing the woman to cover if it is deemed necessary. He flatly forbids men to cover, but women operate in freedom if not covering would shame their husbands.
10 For this cause ought the woman to have power on [her] head because of the angels.
But whose decision will it be? Will the man or the woman decide whether she should cover herself? Paul gives the woman power to make the decision for herself. He reasons that if her ministering spirits can appear before God uncovered, then surely she who is bought by her Head, and free to boldly approach the throne of Grace, and with open face to behold the glory of God, can make this decision herself.
This is Paul's conclusion in the matter. The rest of his words will clarify his preference in it. Much of what Paul just said by way of allowance, he will now contradict by way of preference. Paul will make concessions to Jewish husbands and wives, but in Christ we have access to better things. You will note that this is a common method of argument for Paul, and so it is a natural fit in understanding this passage.
11 Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord.
Paul doesn't want to make rules that are different for men and women, because they are not ever without each other. Everything before this verse has been "in the Jewish world." Now we begin to talk about, "in the Lord." In the Lord, the man and woman are together in everything.
12 For as the woman [is] of the man, even so [is] the man also by the woman; but all things of God.
Yes, Paul says. The woman came from the man, but even though I just said the man is not of the woman, that's only true in the Jewish world. In the Lord, the man is also by the woman. This is true because both are entirely of the Lord.
13 Judge in yourselves: is it comely that a woman pray unto God uncovered?
Judge what amongst yourselves? Not whether long hair is shameful, but whether the man is of the woman. Are the sisters you love merely second generation photocopies of the image of God? Or are they co-equal with us lofty and exalted men as the Jewish oral tradition would have you believe?
That leaves us with Paul's statement that it is comely that a woman pray to God uncovered. As Oloryn pointed out, the original manuscripts contain no punctuation, and no word reversals to indicate when a sentence is a statement and when it is a question. In English we say, "Are you coming" or "You are coming" so that we can tell which is a question and which is a statement, even without the convenience of the "?." There are no such clues in the Greek, so the translator is bound to determine from context whether a sentence is question or statement.
When Paul clearly states in 2 Cor 3:18 that we all with open face behold the glory of the Lord, we have to assume that Paul here is saying that it is comely for a woman to pray uncovered. To assume that he is directly contradicting himself is without justification.
14 Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?
Again. Drop the question mark. Nature does not teach you that if a man has long hair it is a shame 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.
Continued from 14. Nature also does not teach you that long hair is a glory to a woman. Nor does anything teach us that hair is for women a covering. When only one verse in scripture says a thing, and the Greek is open to two exactly opposite interpretations, it is not wise to choose the one that flies against everything else we know.
16 But if any man seem to be contentious, we have no such custom, neither the churches of God.
And finally, Paul closes the argument. If there is a man amongst you who searches the scripture, and for some reason continues to believe that everyone should be covered in prayer, be aware that no other church covers in prayer at all.
This reading of 1 Cor 11:1-16 is completely literal, and far more consistent with the entire revelation than the standard interpretation. This is consistent with Paul's usual way of arguing. It is consistent with the chapter preceeding it, in which Paul is talking about Christian liberty. It is consistent in glorifying Christ as Head over all.
This passage does not yet say that women should ever take authority over men, but it does say that the man is not the head of the woman with relation to Christ. Christ is the Head of both the man and the woman together. In the case of Jewish marriages, Paul makes allowances, but he revokes them as soon as possible. Paul does not here say anything about headship within marriage, but only headship in prayer and worship, so I will not jump ahead to the Eph 5 discussion. As a matter of fact, I doubt that I will address headship within marriage at all in this series. I want to confine the discussion to leadership in the church.
1 Cor 11 is frequently used to assert that the woman cannot lead the man, because the man is over her in authority as Christ is over the man. That interpretation is measured and found wanting.
Next, we move up a little further in 1 Corinthians.