Homily 26 of St. John the Chrysostom on verse IV of I Corinthians...
Ver. 4. "Every man praying or prophesying having his head covered, dishonoreth his head. But every woman praying or prophesying with her head unveiled. dishonoreth her head."
For there were, as I said, both men who prophesied and women who had this girl at that time, as the daughters of Philip, (Acts chapter 21, verse 9) as others before them and after them: concerning whom also the prophet spake of old: "your sons shall prophesy, and your daughters shall see visions." (Joel chapter 2, verse 28. Acts chapter 2, verse 17)
Well then: the man he compelleth not to be always uncovered, but only when he prays. "For every man," saith he, "praying or prophesying, having his head covered, dishonoreth his head." But the woman he commands to be at all times covered. Wherefore also having said, "Every woman that prayeth or prophesieth with her head unveiled, dishonoreth her head," he stayed not at this point only, but also proceeded to say, "for it is one and the same thing as if she were shaven." But if to be shaven is always dishonorable, it is plain too that being uncovered is always a reproach. And not even with this only was he content, but added again, saying, "The woman ought to have a sign of authority on her head, because of the angels."...To be covered he then only forbids, when a man is praying; but the wearing long hair he discourages at all times.
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Men wear no covering because Christ is their Head and they were made in His image and likeness. Women wear a covering because the man is their head and they were made from the flesh of a man. The covering is a sign of the mans authority. The Church teaches that in marriage, the man is like Christ and the woman is like the Church.
I do think TomS does have a point however. It is true that woman covering their head is no longer socially acceptable (as it was only a few years ago and all the ages before that). Today woman, as well as men, are becoming more and more arrogant, vain, and in-human.