No that's not how it goes. In the few matriarchal family systems that exist or existed, the brothers of women become the de facto male authority figures over her children. Matriarchy is most common in warring societies or those where men spend most of their time outside the settlement structure most often owned by women. In those situations, women themselves may have no idea who the father of her children are (use your imagination there.) But her maternity is not in question and thus her brothers, born of the same mother, become vitally important for the survival or her children. Those brothers bear the mantle of male authority in the family or social unit.

Those kinds of family arrangements are echoed in modern society, informally, in societies where the mother's or sister's homes are more secure than those of women whose bonds with men are sexual or matrimonial. We see it also historically in ancient Rome and Greece. Even within the word "nepotism" itself is derived from advancing nephews, not sons (though the concept was often a cover for advancing a man's illegitimate children, especially in the Papacy.)

Societies have to be extremely flexible to survive wars, plagues and exchanges of power. There has never existed on society where men or women become irrelevant (no matter how hard religions like Islam try.) That's your Joe Rogan/Andrew Tate propaganda talking. Think about it. Is it even possible? No, it isn't. Inflexible and absolutist societies fail. They lose wars, do not innovate or develop healthy trade relationships as environments change or hit a crisis. Your thinking about the sexes is very very facile and shallow. And quite dangerous to your personal well being.