Heads, Hats, Hassle?

1 Corinthians 11:2-16

2I praise you for remembering me in everything and for holding to the teachings, just as I passed them on to you.

3Now I want you to realize that the head of every man is Christ, and the head of the woman is man, and the head of Christ is God.

What does head refer to here?  Is it about hierarchy?  (Leadership/ Creation order/ Source)

4Every man who prays or prophesies with his head covered dishonors his head. 5And every woman who prays or prophesies with her head uncovered dishonors her head—it is just as though her head were shaved. 6If a woman does not cover her head, she should have her hair cut off; and if it is a disgrace for a woman to have her hair cut or shaved off, she should cover her head.

What does head refer to in each case? Why does it dishonour?

7A man ought not to cover his head, since he is the image and glory of God; but the woman is the glory of man.

8For man did not come from woman, but woman from man; 9neither was man created for woman, but woman for man. 10For this reason, and because of the angels, the woman ought to have a sign of authority on her head.

Why did men want to cover their heads?  Why did women want to uncover their heads?

What was Paul’s overall concern?

11In the Lord, however, woman is not independent of man, nor is man independent of woman. 12For as woman came from man, so also man is born of woman. But everything comes from God.

13Judge for yourselves: Is it proper for a woman to pray to God with her head uncovered? NO

14Does not the very nature of things teach you that if a man has long hair, it is a disgrace to him, YES

15but that if a woman has long hair, it is her glory? YES

For long hair is given to her as a covering. 16If anyone wants to be contentious about this, we have no other practice—nor do the churches of God.

Why does the length of hair matter to Paul?  Why did women want to cut their  hair short?  Why did men want  to grow theirs?