I think the much better argument is that no society is known to have practiced matriarchy as strictly as is common in patriarchy. Iconic matriarchal societies leave men with plenty of freedom and areas of power that are respected by legitimate authorities.

Matriarchy in popular consciousness is often a geist. A threat of emasculation told to men whose power stems solely from their manhood and thus conflate the two.

Matriarchy as an inversion of patriarchy exists solely within the realms of speculative fiction and pornography.

This isn’t to support matriarchy, I wish to abolish all expected roles based on gender, and I do think that if a matriarchy were to replicate patriarchy it would be founded by victims of patriarchy, but the nonexistance of such a system should be remembered