The vast majority of people, men or women, will agree that of the two sexes, men are by far more likely to revolt than women. Women are more risk averse, more willing to accept privation, and naturally prone to obedience. Even the most radical feminists don't dispute this, though the last observation may rustle feathers.
I am not sure if feminists admit this, but it's also well documented that men are far more honor driven than females. A slight to a man's honor or sense of fairness is far more likely to elicit a violent reaction than a slight to a woman's "honor." I use quotes not to be dismissive per-se but to highlight that women generally do not talk about personal honor much if ever at all.
If you were a tyrannical regime, it makes complete sense that you would promote women to positions of authority wherever you could get away with it because of this. More men means more people you need to respect and more risk of revolt if you trample upon their sense of dignity. Imagine a society completely staffed by women. It would be a tyrant's wet dream.
And the fact of the matter is that the tyrant will always be a tall man. Women, and men too, are predisposed towards obeying the tall and the strong. Furthermore, women do not possess the drive to dominate that men do. So the dictatorship we are careening towards is the classic harem anime/manga. One man ruling a society of women. The perfect dictatorship.
Now, that's all well and good, but is rebellion good or bad? I say that it is good. Elites who fear their population are far more likely to allow liberties than those who are sure that the population will accept dishonor and poverty without complaint. Thus, a patriarchal society where females do not participate will actually be more free and prosperous for everyone than a society with maximum female participation and feminism.
Therefore, we may conclude that females are inferior insofar as they make good civil servants and citizens.