No. War's importance is what determines the degree of patriarchy; roughly speaking. This is a general rule and its sociology's best explanation so far.
I mention the mongols because they weren't male centered much at all compared to the middle east, and there are good reasons for this. The mongols were war-like but war was not so important as to determine their survival. They warred with China in a kind of symbiotic/parasitic relationship (its not quite clear historically how much animosity actually existed and post Genghis Kahn the Mongolian Empire became Chinese since most of the institutions were Chinese in origin). In the middle east war was required in order to survive because virtually all of your neighbors were trying to kill you. The mongols were pastoral but were not sedentary (pastoralism is an economic model which utilizes primarily free ranging animals like sheep or yak) and had far more room to move around. As such they were under far less population pressure to compete for resources. Less competition means less importance for war.
Again, with the native americans. There was a HUGE amount of land area to work with. There was FAR less competition for land and resources. You can be war-like without war being an important institution. There were tribes of pacific islanders that would go to war every few years just for the hell of it. Literally. They would do it for bragging rights and whose status was highest on the island. You can go to war a lot without actually making war important. Competition for resources leading to needing war is what does it.
The more war is needed the more specialized your war tasks become with the accompanying consequences of females being used less and males being used more. Your institutions will tend to reflect this necessity. This means things like religion, family, economy, polity etc will all start to reflect the necessity of war.
Egalitarianism is a variable function. There is not a 1-1 correlation between importance of war and the degree of patriarchy, but it is the strongest correlation we have. Sexual taboos, family structure, local resources, total arable land area, etc will all contribute towards relative importance of male versus female. But if you want to know what causes an extreme of patriarchy, then you need but look at war.
MTF
