"If anyone is inclined to dispute this, we have no other practice, nor do the churches of God." vs16

This is a serious issue. We must not think it small to have disorder in the church.

First, Paul says that in the church [no women pastors] and in marriage, sisters are under brothers and must respect their authority [vs6-10].

If a woman does not cover her head [submit to authority in the home and church], she should have her hair cut off. And if it is shameful for a woman to have her hair cut or shaved off, she should cover her head. A man ought not to cover his head [be ruled by his wife], since he is the image and glory of God; but the woman is the glory of man. For man did not come from woman, but woman from man. Neither was man created for woman, but woman for man. For this reason a woman ought to have authority on her head [the head of the woman is the man], because of the angels.”

This has caused contention, because women have been cursed to despise being ruled [Gen 3:16]. It's the sin of Vashti and must be replaced by Esther's spirit. Obedience helps us see God, that He is gracious and provides for everyone who submits [1 Tim 2:11-15].

Secondly, men must not despise women and rule cruelly [vs11-12].

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

Men have been given authority, but we came from mothers, so we’re to honor the women. No godly husband is a tyrant, even as God told Abraham to listen to Sarah [Gen 21:12]. Her counsel is regarded, and so is her welfare, or your prayers are hindered [1 Pet 3:7].

Thirdly, the text has nothing to do with hats. The head of the woman is the man, even as the head of Christ is God [vs3-4].

“But I want you to understand that the head of every man is Christ, and the head of the woman is man, and the head of Christ is God. Every man who prays or prophesies with his head covered dishonors his head. And every woman who prays or prophesies with her head uncovered dishonors her head,”

Christ submitted to God, even as the man submits to Christ, without bowing to his wife's rule.

Paul's teaching us that rebellion is unacceptable! We cannot be saved on our terms. Despising authority offends even the angels [vs10]. They are ORDERLY BEINGS who do God's will, as must we, if we are Christians.