“there are numerous “one another” verses in the New Testament. “ Yes, but “these “one another verses” do not mean male headship isn’t a doctrine and a tradition of the Apostles. It does not mean that women are NOT to do anything such as caring for others or protecting or providing or anything that is noteworthy. No! it does not mean she sits and waits for instruction.
I recall Mary telling Jesus to do something about wine and Mary telling the servants, whatever He says to do, you must do. Mary’s initiative saved the wedding. Yet Jesus did what was traditional of having a man to protect and take care of a woman- His mother.
The proverbs 31 woman also took care of… and protected her OWN house hold yet she did so under a Patriarchal framework where her husband was known in the gates. One another does not mean there is NO headship authority, for, yet in Ephesian v22 the Wife is singled out to be submissive to her own husband, even though v21 said “ one another”.