Matriarchy is impossible under capitalism. It works like this:
For about two million years prior to the rise of agrarianism, our genus has been either anarchic, matriarchal, or both. This occurs as a result of biology: we are driven by libido (in the Freudian sense of the term) to pursue genetically-superior offspring. In any species, the sex which devotes the most of its resources to the offspring does the choosing, while the other sex does the competing. In humans, women contribute the most resources to offspring, so they are responsible for selecting among men for superior genes. (This all occurs on an unconscious level of course; all the female is aware of is that Strong, Handsome Hunter makes her loins moist and receptive while Pale, Sickly Runt does not.) Since any number of females can share a single desirable male, there need be no competition for mates – all can have his genes who want them for her offfspring.
So far so good. Then came the Agrarian Revolution.
As hunter-gatherers, there not only is no such thing has property, but even the concept of property is impossible. No one saves resources for later because there’s neither need for it nor ability to do so. When resources run short in any given area, the hunter-gatherer simply moves to a different location. Then people discover how to grow their own crops and suddenly you have an extremely different set of needs. The community can no longer leave, so seeds must be saved from year to year in order to sow next year’s crops. These seeds must be protected between seasons, or the community starves and dies. Since women are too valuable to risk as guards, only males can be permitted to become soldiers (since so long as even a single male survives, the community can repopulate itself in a single generation).
Valuable warriors must now find some way of guaranteeing their genes will propagate. Since the only way to be absolutely certain it’s your genes at work is to have exclusive access to a desirable female, women must be turned into chattel, property.
And thus the Patriarchy was born, leading ultimately to the oppressive tyranny of worldwide capitalism.
Fortunately, all this is ending. Every few thousand years, humanity reinvents itself as the current “operating system” of the human brain becomes incapable of handling the growing levels of complexity. The last time this happened was in the switch from hunter-gatherers to agrarianists, when we invented consciousness and the story-cycle of the Hero (as described by Joseph Campbell and Carl Jung), characterized by extreme individualism and male domination. This was necessary because a sense of personal identity is required to enable the specializationation needed for a city to exist. (This phenomenon is described in detail in Julian Jaynes’ Origin of Consciousness in the Breakdown of the Bicameral Mind.) Now, we know from rapidly-accelerating levels of dysfunction in the form of autism, sociopathy, depression, and manic-depression that the consciousness required for a paleolithic city is no longer sufficient for a modern Industrial Age megolopolis. The story cycle of the Hero, the idealized Randian individualist, is coming to its end even as we speak. Capitalism is crumbling all around us, even as the Patriarch struggles to prolong his tired, dysfunctional reign.
I for one am looking forward to the revolution in consciousness which is looming before us, not at all coincidentally as we also see the Singularity closing in on us, the point at which the curve of technology goes vertical and we become essentially our own Gods.