More than just a mirror

Inspired by multiple internet conversations, some of them older than others:

What could or should go into the worldbuilding of a plausible matriarchal human or humanoid society? I've read some stories set in societies that other people have labeled matriarchal, but most of them haven't worked for me, either because I find the worldbuilding itself weak or because the society turns out upon closer inspection not to be truly matriarchal. Here are my thoughts, in no particular order, about what doesn't work and what might work in building a world where it might plausibly be necessary to smash the matriarchy instead of the patriarchy.

( Long, rambly thoughts )