What do you think the root is Vestal?
My theory is that it is men's womb envy.
Patriarchy must have started around somewhen when men decided that they should have a right to control women's reproduction.
I mean, you could say they just started to rape because it felt good to them, some mammal males do, but some random rapists don't make a patriarchy.
Besides, in some patriarchal societies the rape of male children is so widespread that one really cannot say the men rape women because they like raping. They rape women for reproduction and children for "fun".
And because no woman in her right mind would want to be pregnant all the time, patriarchal societies soon became more numerous than equal ones, and spread patriarchy around like a plague. (There's theories that say that many children are more useful in agricultural societies than in hunter and gatherer ones, but I don't think any sane women wants 20 children, unless perhaps she has abnormally easy pregnancies and births)
Patriarchy means "rule of the fathers". Well, in an equal society, there is no such status as "father". There's the man who contributed his sperm, and no one except perhaps the mother knows who that is. And then there might be a man who helps raise the children, but has no claim on them.
A father, who legally owns children - that happens only in patriarchy. And that's why I think men created patriarchy specifically for that purpose.