How did women come to be seen as the inferior in cultures around the world for thousands of years?

I understand the effects of patriarchal scripture (i.e. the Hebrew Bible, New Testament, the Qu'ran), but that cannot account for the rest of the world that does not abide by such scripture. It is because women have naturally less muscle m than men (broadly speaking) and were thought to be not strong enough to survive in society without the protection of a male? Why was (and is) this idea so prevalent in societies around the world? What is it about women that makes people believe they are inferior? Or, rather, what is it about the patriarchal mind that allows it to view the female as subordinate?