Only God has that authority. The only leverage biblical headship has is the leverage of love. One of the first things we learn by observing Jesus is that He Himself recognized the divine order and submitted to it. He acknowledged the headship of His heavenly Father. Man is the head of woman by divine appointment.
Headship has nothing to do with intelligence, gift, ability, or maturity.
It has to do with being a man. Man is not more free to abandon his post than a woman is to usurp it. The divine order is not our choice. That is one of the first things that Jesus teaches us about headship, and that we must embrace when we become His followers. God's order, if followed, will eliminate all quarreling, fighting and bitterness.