Yes there are matriarchal societies, but not in teh majority. I think nature is vast and there are all sorts of different behaviours and social organisations between animals. For example, teh cuckoo leaves its children to be brought up by other birds, but it is in teh minority among birds. I think nature carries out experiments with different social organisations and human matriarchal and patriarchal societies are different ones, but patriarchy is teh most common one among humans worldwide.
I think the witch crazes were about power and the Church imposing its dominance in all spiritual and healing fields. But the Greek and Roman religions were before the Christians and were also patriarchal, although they did have goddesses. The Christian church became even more patriarchal than the older pagan religions.
I think men are programmed to that, like animals in nature are. But they can be conditioned out of it by socialisation and that is where marriage, a stake in society, national and military service are used to condition men to society's needs. 100 years ago men weren't present at teh birth of their children, but now through socialisation they are. Things change and men are changed by society. Yes it is logic and reason that have created societies over millenia with systems of law and justice, rather than teh barbaric rule of teh tribal chief.
But, wars will never end, because wars are about power and men are programmed to seek power. One day drugs will be used to sedate them and stop them getting power, but teh people who administer these drugs will be the ones in power. Power will never vanish and those who get power will always have that ruthless animal streak.
All we can do is seek to make society fairer, kinder and more equal. But we will never have a perfect world, because at heart humans are animals and have an underlying animal logic of survival, which is nature "red in tooth and red in claw".