Hmm?
I guess to prevent some kind of revolution by the masses of unmarried women, the royal family basically promoted the fiction that women hold much of the power in the academies? Then they granted the wives of the feudal lords extra privileges, and it went out of control from there.
So they chose to culturally shift the power to women (a little, originally as a tactic) intending to weaken the ambitious and warlike feudal lords, not because women are less capable or incompetent, but because they're less warlike, less military power-hungry and are more likely to use their talents in non-military areas, reducing the military problems the royals have to deal with? But they overdid it, and the women started indulging in luxury instead.
I guess that explains the discrepancy on why women are supposedly powerful and society, matriarchal in their country, but for some reason it was still a
kingdom ruled by a
king! Also works to explain why the uppermost nobles like dukes and their families remained mostly patriarchal, like Ange's own family.
It was a royal conspiracy to centralize power towards the royals and away from the ambitious and more numerious lower ranked nobles who were a constant threat to their military power.
But certain things still don't line up. Like, if there were way fewer men in the kingdom, then I don't understand how they defeated the law of supply and demand and somehow make the men basically unwanted second class citizens, even as they'd normally be sought after by the many women who wanted to marry. You can't have reverse harems in societies with very few men and many women: the numbers simply don't work. Or does this demographic imbalance only apply to humans, and male demihuman slaves were brought in to fill the demand for the missing men?
Furthermore, maybe this also really only applies to noble society and the numerous commoners are not included. If so, then the statement "women hold all the power" and word "matriarchal" all turn out to be big lies by the royal family that they teach to noble children studying at the academy.
After all, most of the things we've seen so far are from the POV of a noble living in noble society. Maybe we're just seeing a microcosm of their world from Leon's POV.
But maybe a simpler explanation is that, the author realized the "women holding all the power" plot point got forgotten/wasn't consistently applied to the story, people pointed out that kings and dukes still held real power, and was thus forced to write this convoluted conspiracy to explain the discrepancies in the writing... Author, maybe:
Oopsie! I forgot society was supposed to be matriarchal, but wrote it happening in a kingdom ruled by a king, and wrote Angelica living under the power and protection of her actually powerful duke father instead of supposedly powerful duchess mother.
the 
