Um, there are societies run by women.
They called matriarchal societies. Example of one is a tribe in China called Mosuo. In this tribe, the inheretence is passed from mother to daughter (or from female relative to female relative), women can choose mutiple partners and there's no stigma attached to this, male partners hardly have a part to play in the upbringing of the children, the children take the mother's name and there's not a word for husband or father in their local language.
Other women led societies include:
Garo people, India and Bangladesh
Nagovisi, New Guinea
Sarmatains, Ukraine and Northern Russia
Bribri, Costa Rica
Do your research.