The prescriptions about covered heads for women and uncovered heads for men are in 1 Corinthians 11. The logic is very tortured, so rather than me gussing at the meaning, here it is, KJV:

3 But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.


4 Every man praying or prophesying, having his head covered, dishonoureth his head.


5 But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven.


6 For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered.


7 For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man.


8 For the man is not of the woman: but the woman of the man.


9 Neither was the man created for the woman; but the woman for the man.


10 For this cause ought the woman to have power on her head because of the angels.


11 Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord.


12 For as the woman is of the man, even so is the man also by the woman; but all things of God.


13 Judge in yourselves: is it comely that a woman pray unto God uncovered?


14 Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?


15 But if a woman have long hair, it is a glory to her: for her hair is given her for a covering.


Okay, Paul. Whatever you say.

Nice hat, Aretha!