This is the chapter that is used to "justify" women covering their heads:
From the ESV:
Head Coverings
2 Now I commend you a because you remember me in everything and b maintain the traditions c even as I delivered them to you. 3 But I want you to understand that d the head of every man is Christ, e the head of a wife 1 is her husband, and f the head of Christ is God. 4 Every man who prays or prophesies with his head covered dishonors his head, 5 but every wife 2 who prays or g prophesies h with her head uncovered dishonors her head, since it is the same i as if her head were shaven. 6 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. 7 For a man ought not to cover his head, since j he is the image and glory of God, but k woman is the glory of man. 8 For l man was not made from woman, but woman from man. 9 Neither was man created for woman, but m woman for man. 10 That is why a wife ought to have a symbol of authority on her head, because of the angels. 3 11 Nevertheless, n in the Lord woman is not independent of man nor man of woman; 12 for as woman was made from man, so man is now born of woman. And o all things are from God. 13 Judge for yourselves: is it proper for a wife to pray to God with her head uncovered? 14 Does not nature itself teach you that if a man wears long hair it is a disgrace for him, 15 but if a woman has long hair, it is her glory? For her hair is given to her for a covering. 16 p If anyone is inclined to be contentious, we have no such practice, nor do q the churches of God.
Now, there are 13 translations of this, plus the NWT of course, but I wanna focus on the last part, where Paul says that," If anyone is inclined to be contentious, we have no such practice, nor do the churches of GOd.
The NWT translates it thusly:
16 However, if any man seems to dispute for some other custom, we have no other, neither do the congregations of God.