The OP is wrong. While it has often been theorized that there were matriarchies lost in time, you'd be right in saying there's no firm proof for such societies.
There are, however, several
matrilineal and matrilocal societies historical and contemporary. In these societies, the family is traced through the female side and property is sent via the female's line.
Now, in most of these societies there's also a hierarchy where men are present - and almost always in some form of political authority. But then again, the men in political authority are acting upon representatives of a family in which women have all the property and symbolic power.
Regardless, this is enough to through your premise out. Were it not, then we could also point out that gendered divisions of labor are almost entirely obsolete (though not entirely) as a result of the industrial revolution.
Alis Volat Propriis; Tiocfaidh ár lá; Proletarier Aller Länder, Vereinigt Euch!