I lived there for 2 decades and I just don't see it. Women run the home and social life and mostly control the money. Oh hell, you may be right. Men congregate, drink tea and talk politics. It just doesn't look like matriarchy on the surface... But in reality it is. But, the outside world rants about women's rights in the middle east.Scientists. Smith is an orientalist and philologist.
There is nothing surprising here. The whole world to the West from Media was then like that. Everywhere there was matriarchy and chthonism. This is an ancient agricultural culture.