Well this is interesting, but what you always have to keep in mind with the Fathers is that their teachings started getting a little off in various areas as time progressed. I value the writings of the early Fathers, but I never take them as holy writ. Depending on the issue, they could be off. Best to stick with Paul's actual teaching, and again, as is clear from the context, he was not talking about women but wives.
Let me quote it again first:
1 Now I praise you, brethren, that you remember me in all things and keep the traditions just as I delivered them to you. 3 But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God. 4 Every man praying or prophesying, having his head covered, dishonors his head. 5 But every woman who prays or prophesies with her head uncovered dishonors her head, for that is one and the same as if her head were shaved. 6 For if a woman is not covered, let her also be shorn. But if it is shameful for a woman to be shorn or shaved, let her be covered. 7 For a man indeed ought not to cover his head, since he is the image and glory of God; but woman is the glory of man. 8 For man is not from woman, but woman from man. 9 Nor was man created for the woman, but woman for the man. 10 For this reason the woman ought to have a symbol of authority on her head, because of the angels. 11 Nevertheless, neither is man independent of woman, nor woman independent of man, in the Lord. 12 For as woman came from man, even so man also comes through woman; but all things are from God. 13 Judge among yourselves. Is it proper for a woman to pray to God with her head uncovered? 14 Does not even nature itself teach you that if a man has long hair, it is a dishonor to him? 15 But if a woman has long hair, it is a glory to her; for her hair is given to her for a covering. 16 But if anyone seems to be contentious, we have no such custom, nor do the churches of God.
If read strictly (as referring to all women), this would mean he was saying that the "head of every woman" alive is "the man." Which man? This would mean you have a head over you right now, and have to go searching for someone to fill the position. Some would say, "her father." What if your father is dead? The teaching makes zero logical sense unless it is specifically about husbands and wives.
Let me now retranslate the passage as it should actually read:
1 Now I praise you, brethren, that you remember me in all things and keep the traditions just as I delivered them to you. 3 But I want you to know that the head of every husband is Christ, the head of wife is the husband, and the head of Christ is God. 4 Every husband praying or prophesying, having his head covered, dishonors his head. 5 But every wife who prays or prophesies with her head uncovered dishonors her head, for that is one and the same as if her head were shaved. 6 For if a wife is not covered, let her also be shorn. But if it is shameful for a wife to be shorn or shaved, let her be covered. 7 For a husband indeed ought not to cover his head, since he is the image and glory of God; but wife is the glory of the husband. 8 For man is not from woman, but woman from man. 9 Nor was man created for the woman, but woman for the man. (He's talking about Adam and Eve here). 10 For this reason the wife ought to have a symbol of authority on her head, because of the angels. 11 Nevertheless, neither is he husband independent of the wife, nor the wife independent of husband in the Lord. 12 For as woman came from man, even so man also comes through woman; but all things are from God. 13 Judge among yourselves. Is it proper for a wife to pray to God with her head uncovered? 14 Does not even nature itself teach you that if a man has long hair, it is a dishonor to him? 15 But if a woman has long hair, it is a glory to her; for her hair is given to her for a covering. 16 But if anyone seems to be contentious, we have no such custom, nor do the churches of God.