Never more quickly have I realized that there is no point in discussion. There are too many things I'd need to explain to make this anywhere near worthwhile.
I'll just point out a few things and then I'll be on my way. This is nowhere near enough to explain everything to you, but I feel the need to give you a few more pointers.
First of all, it would be common courtesy in any fruitful discussion that if you require me to provide evidence or some sort of logical construct supporting my theory, that you would do the same for yours first.
Secondly, you make the mistake of thinking life is easy. It's a really healthy attitude, and it is certainly born out of real life experiences, but the unfortunate truth is, that it's not easy. It's terribly complicated, and everything has so many reasons that it makes it pointless to try to enumerate them. I only ask that you don't restrict yourself to a single reason, like you did in your post. I only ask that you recognise that life is not easy, and that discussions are not easy and that you can't possibly ever understand a problem fully.
Your simple request for evidence to reject equality of gender as a requirement for peaceful societies is not simple to answer. This question is really a symptom of what I pointed out before. Your question would require extensive research into gender history, statistical analysis of marriage data, sexual encounters, the change of laws over history, how governments evolved under different societies, how governments treated genders, how that affected them, and many more personal assessments like how equality is historically always fought for and therefore it would be a pointless battle to reject it in the long run, ...the list is endless.
I hope you can now see that discussion is pointless. What we are all left with is the belief that we can achieve stable peace, that we can achieve gender equality and at the same time maintain a thriving society. This is what I want, and therefore I try to find theories to support that. Do not take that as naivety. Many will, but only people who have thought this through will agree that all their facts are in essence belief. You are doing the same thing, but labeling it differently. It's like the chicken or egg problem. What came first, your belief or the fact? In order to form any sort of belief, you need facts. In order to find facts, you need some beliefs first.