Several places in the New Testament, had ‘headship’ been God’s intention, it would have been stated and described. Rather, in those places we find no such direct statement and, in fact, other descriptions of marriage indicating full equality.
Two such places are as follow. In 1 Corinthians 7:3-4, when Paul states that the husband’s body belongs to his wife and and wife’s to her husband, no distinction is made between the two parties, in spite of the fact that the word ‘authority’ is used.
The second, 1 Corinthians 7:32-35, concerns itself with the value of staying single in the culture of the time. It talks about a married man being ‘anxious about the affairs of the world and how to please his wife’ (NRSV), and then the same words are used for a married woman wanting to please her husband, therefore being divided in interest rather than single-mindedly serving God. Paul states ‘I say this for your own benefit, not to put any restraint upon you, but to promote good order and unhindered devotion to the Lord.’
Surely these two sets of verses would have been ideal opportunities to state roles of husbands and wives if that had been Paul’s intention and belief. However, instead of even a hint of hierarchy, there is instead total mutuality and consideration.