In light of 1 Corinthians 11:4, why would the Old Testament priests wear a head covering? Why is creation order referenced in favour of the woman being covered and the man not?
This text is from a letter written by David Gooding in 2012.
The answer to your first question—'Why would the priests doing the work in the tabernacle/temple have a head covering?'—seems to me to be that, in Old Testament days, they didn't have Christ. They served God, but they had no personal relationship with Christ. The reason why Paul says that men should not be covered in 1 Corinthians 11:3–4 is that the head of every man—that is, every male—is Christ. That alters the Old Testament position completely, and every man praying or prophesying with his head covered dishonours his head—that is, he dishonours Christ.
Even in modern synagogues, the men wear hats of one kind or another. Orthodox Jews, when going about their daily work, wear a skull cap, in case they should come across the word God in print anywhere. And for that reason, in the synagogue itself, where God is to be praised, they are very scrupulous about men wearing some head covering, a hat or otherwise.
It is different with Christianity because we are related not only to God but to Christ; and we are told that, if any man praying or prophesying covers his head, it is a shame. He dishonours his head—that is, Christ. If you were to explain to an Orthodox Jew why they make the men wear hats of some kind or other in their synagogue, and as Christians we don't make men wear hats—they pray to God without a covering because the head of a Christian man is Christ—an Orthodox Jew might take offence. He, of course, does not accept the deity of Christ, and regards it as the great sin of Christianity that a man, Jesus, is equated with the eternal God.
In your letter, you draw the analogy between priests in the Old Testament who were representative of the people, and as representatives of God were for the glory of God, and yet they wore hats; and you ask why Christian men in the church would be different from that, since they surely are representatives of God on behalf of the people. The straightforward answer to your question is again the matter of the Messiah, Christ. A man in the church does not merely represent God, he represents Christ; and that is the difference.
The second part of your question is a very interesting one. Paul goes back beyond the foundation of Judaism to the original creation, before the Old Testament priestly order was instituted. Why, then, does Paul trace the reason why a Christian woman does wear a head covering in church back to the order of creation? The answer that Paul himself gives from 1 Corinthians 11:8–10 is the order in which male and female were created.
In chapter 1 of Genesis, woman is made equally as man in the image of God, and in that chapter the image of God implies, among other things, having dominion over the animals. Now, that seems to me to remain important. A human female, vastly superior to an animal, has equal dominion over the animals with man.
But in the second creation story, as Paul points out in 1 Corinthians 11:8–9, the male was first made, and only subsequently was the woman made. As Genesis 2 describes it, the woman was made for man. 'It is not good that the man should be alone, I will make a help worthy [or meet] for him' (Genesis 2:18). The woman was made for man, not man for the woman. That, likewise, is one of the reasons why it is said in verse 10 that the woman ought to have a sign of authority on her head. Moreover, man was the glory of God and the woman was the glory of the man. We should notice the term 'glory'. In the presence of God, man veils his glory.
The third reason that Paul gives engages what we call 'daily life'. In the creation story, man was made first, then Eve was made for Adam, and not the other way around. But in daily life, which Paul deals with in 1 Corinthians 11:11–16, the woman has not come into existence without the man, nor the man without the woman. All men have human mothers; and, as far as this goes, birth as a human being is dependent on both man and woman. As I said, all men have human mothers, and this of course is again according to God's intention. Though 1 Corinthians 11:12 sums it up: 'For as the woman is of the man, even so is the man also by the woman; but all things of God'. In this respect, that is the equality of man and woman: man is utterly dependent on woman for his very existence.
That said, at the level of daily life, there are still distinctions between male and female. We can all think of many, and it is proper that the distinction between male and female be indicated.
Of course, not all women have a good head of hair. But, if a woman does have a good head of hair that is yet another reason for her to cover it in the church. Why? Because that head of hair is given to her as a beautiful mantle—a glorious thing to look at; but in the presence of the church she is asked to veil her glory so that it should not distract from the main person present, who is the Lord.
With love in Christ,