"Hard-wired" is a strong claim. No one in this thread has denied that patriarchy is common; it's the claim that it is absolute and "natural" that we find very dubious. No, if there multiple exceptions to the rule, it's not "hard-wired" in, even if those exceptions don't make up a global majority at the moment. There are other cultural near-universals, and that isn't surprising given that humans talk to each other and spread ideas around.
Is it really a strong claim? It's not controversial that we're partly ruled by instinct. We're also hard-wired to prefer fatty and sugary things. Which is why so many people are obese. We're hard wired to want to feel happy feelings. Which is why addiction is a thing. How aren't you saying that all fat people are fat by choice and all addicts want to be addicts? Clearly some things are hard-wired and natural.
Something being hard-wired or instinct, just means that we are systematically nudged in a direction. Anybody can avoid eating cake if they put their minds to it. But over time, fat people are more likely to fail at resisting. That's what something being innate or natural means.
Nobody in this thread has claimed that this effect is absolute. You just made that up. There are plenty of female leaders in the world, and they have done a stellar job. Nobody in this thread has challenged this. So in what way is anybody in this thread claiming that the preference for male leaders is absolute?
I think you are making the black and white fallacy in this thread. I think you are interpreting the statements you don't agree with as being much stronger than they are, in such a way that they are easy to refute. Without actually replying to what is being said.
All kinds of nonsense ideas get spread. But they are constantly tried and tested all the time. Ideas that don't solve problems, or are perceived to solve problems won't be retained in a population. What's in it for the ladies with patriarchy? Why would 51% of the population, up until the modern age, put up with being reduced to property? If you claim that all it took was a conspiracy of men, I'd say you don't have enough respect for the intelligence and abilities of women. Also you'll need some way to explain why enough men would go along with the patriarchal conspiracy to maintain control? I find it hard to believe that even a majority would do it, unless it's nudged in this direction by something innate and hard-wired.
And I note that you didn't think it was a red herring until you were educated against your will about the nature of Mosuo society. Funny how irrelevant a data point becomes when you realize it doesn't support your ideological projects.
I still have read very little about Mosuo culture. Not enough to judge whether or not you are correct. Either way, it's a statistical population of one. And since they seemed to have male chieftains up until the communist takeover, it makes me suspect that this matriarchy was engineered by the communist party. It brings to mind how the British government broke the Scottish clans during the high middle ages. They gave them enough money to not have to do anything all day, and gave them enough free beer to ensure they were all drunkards. They did this until the clan system had fallen apart and was beyond repair. Without factoring in the "intervention" of the British crown your conclusions of the nature of the clan culture from this period, will be wrong.
A society where men do nothing but lie about all day doing nothing, is not a sustainable society. It's questionable whether this Mosuo culture is a genuine product of real demands of Himalayan mountain life, or engineered by the communist party, and a result of that intervention.
Other Asian hill tribe peoples I know more about is the Zao and the Hmong in Vietnam. I was there in 1996 when most Westerners weren't allowed in. I was one of the first outsiders who had been there since the wars of independence in the 1950'ies. To say that they had been royally fucked over by the communist government is to put it mildly. The Hmong were all drunks. By central government design. The Zao and Hmong were in perpetual conflict, also thanks to central government design. All designed to make the hill tribes less of a problem for the central government. Back then if they ever built a large building the central government wouldn't inspect it. They just sent war planes that bombed it to bits. Which put a lid on attempts to effectivise farming to make some money, and lift themselves out of poverty. That's the degree these hill tribes in communist countries have been treated. It's pretty extreme.