The institutions of human society are Marriage and Family.
What is an "institution"?
"An institution is any structure or mechanism of social order and cooperation governing the behavior of a set of individuals within a given human community. Institutions are identified with a social purpose and permanence, transcending individual human lives and intentions, and with the making and enforcing of rules governing cooperative human behavior."
The institution of Marriage keeps humans distinct from animals, and we desecrate it at our peril. Once we have desecrated Marriage, then a Matriarchy that will mean the death of your culture, society and civilisation follows inevitably.
Marriage is a patriarchal idea, by the way, and that is why Feminism - an ideology of the Matriarchy - has systematically eroded the institutions of Marriage and thereby the Family and thereby Western societies and thereby Western civilisation itself.
And that is why the only good matriarchy is a dead matriarchy. It is the totalitarian statist matriarchy that encourages Slut Single Mums to breed at the expense of the taxpayer and forbids the criticism of Slut Single Mums.
Remember: lower animals are either single-parents or have harems. Only humans have the institutions of Marriage and Family that comes between the two extremes.
Why would we want to live like animals when we can live like humans?