I see that you are on a roll today
There is nothing wrong with a woman wearing her hair long or short. This scripture use to hold some women in "bondage"
But there is deeper "cultural" meaning to this scripture. Start reading from verse 1 - 16 "this is the entire story"
The unvailed women in Corinth were prostitues and many had had their head shaved. The women who had their heads uncovered were also prostitutes. So the sisters in the Church were saying "All things are lawful for me, therefore I will not cover my head"
Paul, says this should not be done because the vail is a mark of subjection, not the man, but to God.
Verses 7-9 - summary
The woman's place is to be a helpmeet [Genesis] to the man [husband]. She is to be the other part of him "no man is complete without his helpmeet" except where God has blessed him for a special work [Apostle Paul] Then it can be argued that Paul, was married. [that is another subject]
Listen to verse 10
We are being watched by God's Angles. "Gurdian Angles"
Are they not all ministering spirits, sent forth to minister for them who shall be heirs of salvation?[Hebrews 1:14]
11
The marriage relationship - The power of the woman is to hold her man and vice versa.
12
The become one [Genesis]
This scripture tears down "women lib" for a "Christian" woman. Men and women need each other.
I can briefly explain the rest if you desire.