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It dates back to the Book of Enoch which was not considered to be canonical to The Vatican. Christian women are meant to cover their hair while praying as well.
1 Corinthians 11:1-34
Be imitators of me, as I am of Christ. Now I commend you because you remember me in everything and maintain the traditions even as I delivered them to you. But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God. Every man who prays or prophesies with his head covered dishonors his head, but every wife who prays or prophesies with her head uncovered dishonors her head, since it is the same as if her head were shaven.
1 Corinthians 11:5
But every wife who prays or prophesies with her head uncovered dishonors her head, since it is the same as if her head were shaven.
1 Corinthians 11:15
But if a woman has long hair, it is her glory? For her hair is given to her for a covering.
1 Corinthians 11:3-16
But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God. Every man who prays or prophesies with his head covered dishonors his head, but every wife who prays or prophesies with her head uncovered dishonors her head, since it is the same as if her head were shaven. For if a wife will not cover her head, then she should cut her hair short. But since it is disgraceful for a wife to cut off her hair or shave her head, let her cover her head. For a man ought not to cover his head, since he is the image and glory of God, but woman is the glory of man.
1 Corinthians 11:10
That is why a wife ought to have a symbol of authority on her head, because of the angels.
The Book of Enoch was taken out of the Bible, but the reasoning behind women covering their hair is so that the fallen angels do not fornicate with them to produce the nephilim as it were during the days of Noah.