Some anthropologists believe that patriarchy became the dominant structure of primitive societies after the invention of nomadic animal herding. People developed a attachments to their flocks, and the offspring of those flocks.
Heck, people 20,000 years ago might not have understood where babies came from! Lord knows that apes don't understand this. Men would have figured this out in short order from watching domesticated animals. They would have become much more aware of their biological attachment to their children after becoming herders, and much more aware of protecting his investment in any mate.
Of course, herding is a heck of a lot easier than hunting up your meat every day. So the more successful, dominant groups of people (herders) BECAME more patriarchal than the less successful hunter gatherers.
So patriarchy, rather than creating a successful way of life, is a RESULT of a successful way of life. This is why matriarchy seems to be limited to "fringe" hunter-gatherers. The rest were either wiped out or adopted the new ways.
Well, I wish there were an anthropologist here, instead of schoolteachers and whatever the Hell else everybody is.