But Pearl, outside of some scoundrels, no person with a little bit of reasoning considers such a mandate as hierarchy of inferiority, subjectivity or tyranny. Which is why it is often referred to as Complementarianism.
As much as a child should not try and usurp the position of their parents, as much as a civilian should not defy the authority of a policeman, or any government official, it is improper for a being who was created after another, and as a help to another, to have authority over the initial being. Show me one wise man, and I will easily show you 10 wiser women, no problem, and vice versa. Even children often outgrow, out-mature, or outsmart their parents, it does not mean that they should ever challenge their inherent authority.
This is a call for men to step up to the plate, not to dominate women or children. In my opinion, he is to give his life, not only for his wife, but in any context, for the women and children. Only an incompetent fool (yes, the irony), would think that this principle is an opportunity to oppress women, or consider them as inferior, only a derelict and incompetent fool would hold that position!
I don't know which church you belong to as even the Anglican church allows women to follow their calling as clergy and bishops and long before they allowed that they allowed female lay readers to take services and preach.
And I do agree that men need to step up to the plate and be the leaders Jesus needs them to be; men of honour and integrity, men of faith with the vision and guidance of the Holy Spirit. And men who are not too proud to take their turn on the brew rota or cleaning team.
I know it's really hard for some men to see things any other way but I think they should at least look into it. You could start by reading the book I recommended. Bet you won't though. :)