Why don't Christian women cover their heads today if the Bible says to?
Christian women generally do not cover their heads today because the practice is understood as a cultural custom tied to the environment of the early church, not an unchanging rule for every culture. Scripture remains authoritative, but customs change over time, so the head-covering instructions are read with historical context rather than as a universal requirement.
Les explains that the head-covering issue is one of those areas that is as far removed from us in America today as meat offered to idols. It has changed by virtue of customs and environment. He stresses that the Word of God does not change, but customs do, and God mandated many things for Israel because of their national customs and the way He had taught them. Therefore, these verses should be taken with a grain of salt—not rejected as no longer being the Word of God, but read with awareness that there has been a tremendous change in the position and attitude of men toward women in Christianity. Paul himself was not anti-woman.