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 11:3-16
Introduction
Headcoverings have been a subject of rather heated debate in the last century of western Christianity, and I would like to touch on a few reasons that I believe it is still relevant for today, according to the Scriptures.
Being raised in a pseudo-Mennonite church, I have had to take a large step back from what was taught in the pulpit—most of which was borrowed unapologetically from ther their "historic heritage"—and really examine what God says about it in the Bible. It is far too easy for us to take what we have been spoon-fed and simply regurgitate it. This is not God's method, nor desire for us. He desires that we seek Him and consult His Word for the truth. So, that being said, don't just read this and take my word for it; seek God about it!
Background
I feel the Word of God makes this subject MUCH simpler than the doctrines that are taught in most conservative churches. I feel that it is clear (and most historical cultures also back me up) that a woman (or wife, as specified in the Russian translation) should be veiled when praying or prophesying, in the same fashion that a man should uncover his head. Interestingly enough, our culture has retained half of this tradition. It is still considered rude for a man to wear a hat in church, or during prayer. Additionally, it is interesting to note that the Greek is somewhat ambiguous in this passage. The word γυνή (Strongs G1135) can refer to either a woman, or wife specifically. I personally would lean towards the meaning of "wife," since the 200 uses of the Greek word in the NT mostly refer to married women, or translate the word "wife" explicitly.
Salvation Issue?
Unfortunately—in the quest to defend their traditional beliefs against an increasingly apostate, modern church—many well-meaning, conservative church members have resorted to promoting external, "pet" doctrines far above their Biblical weight.
The Bible does not link the head covering to whether or not you are saved, nor do I think that it is of any more prominence or weight than any other doctrine or precept that is taught therein. It is also most unfortunate, that many of the religions who do uphold the precept of wearing veilings in the western world, place an undue amount of importance on it, thus distracting themselves from the weightier matters of the Bible: i.e. Jesus Christ. Conversely, in most eastern and older cultures, women traditionally cover their heads. It is simply an expected, cultural norm, and not tied to religious significance so much as it is to common, historical femininity.
When you contrast that with the many western women that I have heard talk about this subject, they generally resort to bizarre and irrational reasoning to support their "belief" that head coverings are simply historical garb, and therefore completely irrelevant for today. Sadly, most of their argumentation seems to have come right out of the women's lib movement of the 1960's: a cultural movement driving women to free themselves from a so-called "minority status," into complete equality with men. Again, let me clarify my position. I don't feel at all that women are "lesser" than men; to the contrary, Paul writes very clearly about male and female equality in Galatians 3:28—soul equality. Beyond that, there are differences, and creating physical equality between man and woman is not supported biblically. God, not man, created the headship order, as well as women's gentler, more compassionate nature. For example, men would make terrible mothers. The Bible strongly prohibits men from abusing the authority that they have been given, but rather exhorts them to channel their God-given strength into the creation of a safe haven of honor and respect for the "weaker vessel" to be able to rest within. (1 Peter 3:7)
Conclusion
I also want to mention that I personally feel this conviction should be carried by the woman. As a husband, I can gently and lovingly share my convictions with my wife, but I feel that it is up to her to act upon what she personally feels that God is asking her to do. I am her leader, not her Holy Spirit.
(Adapted from a letter to some good friends)