Frankly, I think your notion that "Government moved from conquering other countries for material gain, to conquering other countries for humanitarian reasons" is fluff in the wind. I notice that World War I, for instance, was sold as a noble, humanitarian crusade to "end all wars."; that the Civil war was for a significant number of Americans a war to end slavery; that the American Revolution for many people was at least as much about the right to self-representation, self-determination, and freedom from tyranny as it was about taxes. Just to name three wars.
But beyond that, I find your notion that selling a war as a fight for humanitarian reasons is evidence of a matriarchy, or at the least, of women's influence on politics, to be unevidenced. I'm curious what possessed you to think that's plausible?
Honestly, your OP doesn't seem to be thought through very well. For instance, you assert that women are the single largest voting block, but that is a huge assumption! Most studies I've seen clearly show that women do not vote as a block. So, I'm left wondering what evidence has persuaded you that they do vote as a block?
Again, you seem to feel that Democrats are the most powerful political party in America. If that's indeed so, how do you account for Republicans being in control of the US House, the US Senate, and all but in control of the US Supreme Court? To say nothing of their being in control of more governorships and state legislatures than Democrats?
You also fail in the OP to clearly define what you mean by patriarchy and matriarchy. Without such definitions you might as well claim anything that suites your fancy is patriarchal or matriarchal. I could be wrong, but I'm guessing you've never really read up on the two or three matriarchies known to anthropologists, and that your notion of what one might look like owes more to your imagination than to any reality.
I could go on -- and on and on -- but the bottom line is your OP struck me as grossly assumptive. It reminded me of nothing so much as a creationist argument against evolution.