Note 3 at 1 Cor. 11:4: Paul is drawing on the symbolic meaning of a custom to make his point that Christ is the head of each member of the Church. Beyond any practical purposes for a veil or covering, these articles of clothing symbolized submission. Man was created directly under authority to no one but God and should therefore not pray or prophesy with his head covered. This signifies his submission to God alone.

On the other hand, the woman was created for the man and told to submit to him. Therefore, a woman wearing a covering when she prays or prophesies symbolizes her submission to her husband as a God-given authority in her life.

So, Paul uses the symbolic meaning behind these customs which these Corinthians used every day, to remind them that their head or authority is Christ, not him.