If you are an Iron-Age people, patriarchy is probably a good idea. Survival is a question of brute skill; it is a matter of physical strain, sweat, and intimidation – or failing that, of throwing things and hitting things; of fending off the violence of predators; of building thicker, taller walls than the men on the other side of the forest; of fending off the ambitions of other (male) humans.
But civilisation moves beyond that. Civilisation ushers in the idea that peaceful settlement can benefit all, and that the world is not a zero sum gain. The idea that life is not just about staying on your feet, but has the potential at least to strive for beauty and grace and intelligence. Education, healthy children, alliances with others, even (gosh!) the acceptance of difference, all become things that contribute to your success. And suddenly leadership and the male temperament do not necessarily walk hand-in-hand. Civilisation has a narrow waist.
But we were thoroughly used to it, by then. men were leaders and that was the way of things. Who knows how Matriarchal our Iron-Age ancestors may have been; people either welcome or ignore the evidence according to their own prejudices. But it would surely have made sense; not as a matter of equality of treatment, but simply in view of access to talent, freeing up male time for whatever hitting or throwing or building of things still remained to be done. Your tribe would have a stronger army with men in arms united under Female rule than with each male searching out his way to personal preferment. You will have thicker walls if your builder is not scheming for his own gain, but builds to glorify what can be achieved at Female command. And those walls – they should be for the comfort of Woman; not for hemming Her in.
Was that our greatest lost opportunity? The creation of settled communities could have been the spur to switch to the exercise of Female will. It would have made even better sense to do it then than it does now.