Created to be Interdependent
Paul had been teaching about headship in the home (1 Corinthians 11:2-10), but in these verses wrote that the male 'head' is not superior or designed to be independent of the woman. He strikes a culturally unsettling note. Most societies give a superior place to one gender, or allow the dominant partner to have the right to rule. But Paul gives the Lord's view that although headship is male, neither gender has everything and that both were designed to be complementary to each other. Both have come from God and neither has the right to dominate the other. They must work together.
Paul argued for a clear distinction between men and women, partly to avoid the issues of gender confusion which were tolerated in Corinthian society, and to honour the Creator God who made us distinctly different - for our blessing and His glory (Genesis 2:21-23). He appealed to an instinctive sense of what is right and wrong.
Of course, as people get into the habit of rejecting God's order for humanity, their God-given 'natural wisdom' becomes dulled and defective, so that they cannot appreciate the Creator's design (Romans 1:21-22). But the Apostle was writing to people who had received the Spirit of God and whose Creator-given instincts should have been refreshed. The glory of a woman's hair is a part of the beauty of creation and should be respected as such.
Confusion about the presentation and function of gender differences often occurs in societies which have rejected the One who created them. And some of that spills over into the churches. So today it is still important for church leaders to be clear about how gender differences should be presented by believers, as a way of honouring the Lord in their community. Hair length was an issue in Corinth; it may be something else where you live. There will always be some who are contentious: but the apostolic principles hold well in every age, and wise spiritual leadership will work them through for the culture in which their churches witness to the Creator-Saviour, the Lord Jesus Christ.