Actually the few matriarchal societies that existed, women were more nurturing and risk averse, and this is why they "existed", patriarchal enemies could easily wipe the floor with them.

Also I remember seeing in the opening of a openly feminist franchise, a women describing a certain matriarchal society that exists in modern day (I forgot their name though :( but it is somewhere in backwater asian Russia), and I got curious and went to research and...

Actually, only the commoners of that society are matriarchal, nobles follow a more or less patriarchal system (men inherit form men, and women from women, most political power of the nobles are with the men though, but there is no formal rule against women having it too), and the nobles enforce matriarchy on the commoners (people do not remember anymore why they do it, but research suggests that the reason was to keep commoners tame and keep them from rebelling)