This meant that familial descent was traced through mothers rather than fathers, which gave women quite a bit of power.

Mama's baby, papa's maybe. Lineage is important when there are mouths to feed. It seems fairly easy to analyze strict religious law, especially in Islam, as a way for men to be sure that the mouths they feed belong to their own progeny. The extensive restrictions on women's behavior assure that they have not had and do not have sex outside marriage. With those rules in place, patrilineal society can be maintained, and with it, make dominance.

This is not to say that under certain environmental pressures, the male as provider/protector and the female as nurturer and supporter is not a more successful adaptation than the Iroquois method would be under those pressures. Societies do not arise and organize themselves in a vacuum; they evolve under conditions. What works in one place or time may not work in another.