As Paul moves from the end of chapter 10 to the beginning of chapter 11, we see how the theme of freedom continues with regard to how men and women relate within the church of Jesus Christ and also in marriage. Although Paul is certainly responding to concerns that had been brought to him by the Christians in Corinth, he is linking his answer with what he said in chapter 10 about freedom. There are restrictions that apply in how each other uses this freedom.
Men and women are created equal in the image of God, so that it is absolutely the case that no woman has to submit to any man as concerns the general realm of creation. But in marriage, when the woman becomes the wife of a certain man, then there is an area of submission in which she willingly commits herself, which Paul teaches is a reflection of that spiritual order we find in the universe. As he writes in verse 3, “Now I want you to realize that the head of every man is Christ, and the head of the woman is the man, and the head of Christ is God.” In other words, in the economy or plan of salvation, Jesus the Son submits to God the Father, even as they are equal in terms of their divine being and nature.
Christian theology speaks of the Trinity, in which each member of the Godhead is equal to the other and is entitled to equal honor and equal glory. And yet, within the functioning of the Trinity, theologians speak of a functional submission of Christ to the Father, and the Holy Spirit to both the Father and the Son. Paul is saying that there is something similar in the relationship between men and women within the church of Jesus Christ.
This is a puzzling section. Not only does Paul make this comparison in relationship between the Godhead and men and women in the church, but he then goes on to talk about their hair length and whether or not it should be covered. But then Paul makes it even harder by telling the Corinthians that the proper hair length for both men and women can be understand from nature. Paul is not giving us instructions that he received by divine revelation as an apostle. These are not hidden truths that Paul is now disclosing as a preacher of the Word. Rather, Paul says that all you have to do is look around you to see that this is true.
Let me explain what I think is going on here. When Paul talks about head coverings, he is talking about a recognition of authority that can be observed even in the natural order of things. This is not to say that in this area of the differences between men and women there are no cultural differences among different places. Certainly there are. But Paul is saying that there are, nevertheless, built-in differences so that men are not women and women are not men. This is obviously a good thing because it is the way God made it.
Then he refers to this matter of hair coverings, as well as the length of one’s hair. Women generally do not cover their hair in church anymore. But it at least used to be the case that at some kind of formal ceremony, such as a Christian school graduation, when the opening prayer was announced, the men would instinctively take off their hats, while the women kept theirs on. Now perhaps that is more of a cultural practice, since such ceremonies are different from a worship service, but in a certain sense perhaps it illustrates the kind of thing which Paul obviously observed to a much greater extent in the culture of his day. He was saying that there is a certain sense in which intrinsically we recognize in different ways the authority that God has set over us within the church of Jesus Christ.

