Sure, some men probably do choose that freely but the vast majority are punished by patriarchal society if they stray from it from such a young age that they have no idea whether it’s actually their way or not. That’s the problem with boxes — they deprive people of free choice. And when some people mock other people for their choices, they no longer experience that freedom and it becomes coerced choices.
Ok, so it’s another technicality that they are not pure matriarchies, but these types of societies are always highly egalitarian, with both males and females having roles of power and respect. Up until 5 thousand years ago, nearly all societies were constructed like this, and were that way from neolithic times. For more learning, check out The Chalice and the Blade by Riane Eisler. “The Chalice and the Blade tells a new story of our cultural origins. It shows that warfare and the war of the sexes are neither divinely nor biologically ordained. It provides verification that a better future is possible — and is in fact firmly rooted in the haunting dramas of what happened in our past.”
Another book with good scholarship along the same lines is “When God Was A Woman” by Merlin Stone.