Headship as Seen in Common Sense & Common Practice

In 1 Corinthians 11:13-16, Paul closes his argument on the importance of women wearing head coverings as a sign of submission to male headship. Paul shows that the distinction between men’s and women’s appearance is natural and divinely ordained and that rejecting such practices reveals a rebellious spirit against God's order. Though head coverings were a cultural expression of feminity and submissiveness, what about the length of our hair? Does God care if men have long hair and women have short hair today?