If you think the only metric of a "superior" culture is being able to defend yourself against armed men on horseback - when previously you had no need to to defend yourself against anyone...

Patriarchy spread because it was so disruptive, not because it was somehow a "better" system. Why would a culture where only certain people count and certain people thrive ever be considered "superior" to one where everyone matters, and everyone eats and is cared for by the community?

Economic models of the spread of inequality (patriarchy) done at Standford University concur.

“In other words, inequality did not spread from group to group because it is an inherently better system for survival, but because it creates demographic instability, which drives migration and conflict and leads to the cultural — or physical — extinction of egalitarian societies."

~New Scientist