How the culture(s) of Corinth probably made head coverings a dilemma for women:
I read elsewhere that men had these 2 messages about head wear: Jewish men wore something on their heads when praying as a sign that their sin stands between them and God. The Christian message is about Jesus forgiving sin, nothing standing between us and God, so Christians should not follow their example for headgear under prayer. Male temple prostitutes in Corinth had long hair, and obviously, Christians should show their religion is not like those religions. That made it pretty clear what men in that world should have on their heads when going to church: Short hair, no extra headwear. Anything else sent out the wrong message.
Women, on the other hand, allegedly got mixed messages in that multicultural society. One message said women are more respectable covered up. That is probably also what husbands in at least one if not more of the cultures at Corinth expected of their wives. (Corinth was a multi-cultural society.) That may explain why they were reminded of being the glory of man – they may need to remember that, except for all people being in God’s image and all believers having the glory of God, husbands are also shamed when they do not cover up.
But another was the one, already mentioned in the previous paragraph, that wearing something on your head is a sign of shame before God. And things of glory are usually not covered up but displayed, and the passage mentions both women and their hair as a glory.
Adulterers had their heads shaven – this was not a choice and society would not allow them to cover their head in the same way married women did. (Some sources say prostituted women in that culture had short hair too, but many other sources disagree.) While some people in that multi-cultural society believed long hair is already enough of a covering, others claimed that long uncovered hair is as shameful as shaven heads.
Not all women in the church were free to wear their hair as they would like, and everyone in the church did not understand the message given by hair coverings/ long uncovered hair the same way. They did know that a shaved head was a sign of shame to their culture, and Jesus takes away shame – even if the culture wants a woman to walk around with a shaved head, in church she should be welcome to wear something on it.
(Some scholars believe what is translated as hair coverings should rather be understood as wearing the hair up – covering the head with your hair – as that is what respectable women did in that society, while prostituted women wore loose hair.)
One terrible translation error that should be avoided
Many Bible translations were translated really badly in verse 10. Period. The text says:
For this cause ought the woman to have power on her head because of the angels. (KJV)
It is for this reason that a woman ought to have authority over her own head, because of the angels. (NIV)
The bad translations say:
That is why a wife ought to have
a symbol ofauthority on her head, because of the angels. (ESV)
Therefore the woman ought to have have
a symbol ofauthority on her head, because of the angels. (NASB)
Even worse is this:
For this reason, and because the angels are watching, a woman should
wear a covering on her head to show she is underauthority. (New Living Translation)
The text, as in the Greek, say a woman should have authority on her head – not “a symbol of” authority. Every text in the Bible which uses this Greek term for authority means the authority of the person spoken of – never that the person is under someone else’s authority! The KJV or current NIV are right: She should have power on/ authority over her own head. Which probably mean that women could choose for themselves what to wear on their heads, considering how to work along with their own husbands’ wishes and the message sent out to their own culture and family.