A matriarchy would be a dominance-based hierarchy where women have more social and political power than men - something that has never existed in humans, although we do have a few modern matrilineal, matrifocul cultures. They tend to be quite balanced and understanding of the importance of both men and women, but I digress. What you are describing is just another manifestation of patriarchy, where women's main function in society is the producing (and subsequent care) of children. The fact that some women uphold and buy into that is not really surprising, since we are all deeply indoctrinated into this social system, and women often uphold patriarchy too.

https://medium.com/inside-of-elle-beau/women-uphold-the-patriarchy-too-c6c2e5de8619