The misunderstanding that the hair is the covering was propagated by those who wanted to follow the fashions. There are two words in the Scriptures, in 1 Corinthians 11, one is the very nature of the woman's hair as her covering the other one is a veil that God commanded the women to wear over her hair when she prays and prophesies in the gathering.
When Paul said "we have no such custom", as has also been misunderstood to fit with the culture, does not say that in the original language. In the Greek that phrase says; "we have no other custom of being contentious about this, all the churches do it."
All the churches practiced the covering up until about the 1960's, the women wore hats to be more fashionable and probably didn't know what the tradition meant or where it came from. My mother didn't know the Bible but she wore a hat to church. The men NEVER were caught in church with a hat on, they took it off when they entered, but they too didn't know why, they thought it was just respect. IF the hair were the covering then the men would have to shave their heads to comply with Scripture. The uncovered for the men in these passages means he is not to have a covering over his head.
In 1 Corinthians 11 the men are commanded to be uncovered, that's why the men took off their hats. However, just as the women lost the meaning of the covering so did the men lose the meaning of the uncovering.
We can see what happens when Bible schools and seminaries attempt to be "relevant" to the times, they begin changing the actual text to say what it does not say. Now we have two generations of people who do not practice the covering because they have been taught the wrong things.
God said that the covering for the woman was to show that she is under the headship of her husband and for the sake of the angels. We are teaching the angels by our conduct. The covering was not just a practice of the time, it was a command of God for all the churches until the end of the age. We know this because in the same passages it calls for the women being submissive to their own husbands. Was that for back then too? No, everything written in that passage was for all time until the end of the age.
When traditions are not backed up by the Bible, they float away gradually because of the changing culture.
Far too many believers listen to teachers instead of seeking God for truth.
Please do not come to argue about this point, just go to prayer and ask God. I cannot be changed and I want no contention on this matter here.