Well that Greece also had a Patriarchy does not mean it was inevitable or how it had to be. Indeed if you read “The Chalice and the Blade” Patriarchy is rather new in the course of Human history . Archeological finds in Turkey so societies that existed several thousand years ago that treated man and woman much more equitably. In the “Chalice and the Blade” the author makes the case that this all changed when violence and brute force via warfare became an accepted form of behaviour inside the species. This lead to the breakdown of the Social norms that existed at the time and ultimately led to the most brutal and violent imposing their will on others.
Human history goes back a lot further than initially thought and many of those older societies did not embrace war as so many do today. We only think it normal because it has been the way things done for a few thousand years too many.
Patriarchy is born in war and it my humble opinion that women will not gain equality by becoming “warriors” and joining Militaries. What has to happen is the Males have to UNJOIN the Military and the embrace of violence and warfare.