Some who have a jaundiced view of male priority often label it chauvinism, which the dictionary defines as an unquestioning belief in the superiority of one's nation or gender. The Bible does not share that view. With priority may come privilege, but there also comes responsibility.
It will be seen from Romans 5:12 that although Eve sinned first, it is maintained that it was by one man that sin came into the world!
So the husband carries the responsibility for the welfare and upkeep of the family. Just as the Church is a large family, so the Christian family is a mini‑church and the father is the shepherd of his little flock. The Bible also states that a church officer must know how to govern his own house, otherwise he is disqualified from governing the House of God, and any who do not provide for their own households are worse than infidels.