Paul used the Greek word, kephale in these passages which has been translated as ‘head’ into English. Head can mean many things in English - the piece of our body that sits on our shoulders, the leader of an organization, an authority figure, the top of something as in head of the bed or beginning of something as in trail head, it can even mean the toilet.
There are other Greek words used by Paul when he is specifically dealing with authority. In 1 Cor 11:10, one of those words used is exousia and is translated correctly as authority. In fact, this occurs only a few lines below the ‘head’ passage. If Paul intended for us to understand 1Cor 11:3 and Eph 5:23 to convey a chain of command or authority, why did he not use the Greek words that denote authority? Instead he uses a word that is used specifically in the language of his day to mean source or origin. And why did translators choose to use the ambiguous “head” with the intent of having it wrongly interpreted?
Prominent false religions of Paul’s day, the worship of Apollo, for example, taught that all life began with the woman. The verses in question state: Messiah is the kephale (source or origin) of man and man is the kephale (source or origin) of woman and God is the kephale (source or origin) of Yeshua. Paul is correcting a false teaching brought in through new converts by stating that man did not originate with the woman. He is clarifying a significant difference between the two religions, NOT making a pronouncement that there is a chain of command that ends with the woman at the bottom. (Refer back to previous posts on the equal partnership of humankind in the grand scheme of YHVH’s plan.)
There is one mediator between YHVH and man (humankind - men and women) and that is Yeshua. If the correct meaning for ‘head’ is authority, then following through to the logical conclusion of the verse makes the man the authority over the woman, inserting him between her and Yeshua. Maintaining the “headship” of the man as taught by two thousand years of church doctrine makes the man the mediator of the woman in place of Yeshua. Perhaps this is why so many men are exasperated. They have been put into a role they cannot fulfill.
If we see the original intent instead of looking through millennium of misinterpretation, many other things become simple and no longer need entire dissertations to explain.