There are two reasons for why these are so prominent.
First, this was tried in Nazi Germany and the Coalition States are meant in many ways to be "Nazi Germany Done Better"; second, because this is a society that--like Orwell--is obsessed with control and one of the oldest ways (old, in large part, because it works) is division of the population against itself and the easiest way to do that is all lines of sex and gender. Removing individuality from the population, getting them to think in terms of being part of a greater--but fragile--whole without which they have no security, works when you institute a Greco-Roman style of patriarchy and make the patriarchs into agents of the state. It's a peculiar sort of neo-feudal social mechanism where you're nothing unless you're part of something bigger than yourself.
Why the repression? In part because of the fear, uncertainty and doubt that it generates- and tyrannies thrive on that anxiety because it opens an avenue of social control. In part out of cold logistical necessity, something the population understands intuitively; the Coalition's playing a numbers game, so it uses force and fraud to maximize the breeding rate knowing full well that it's their specific circumstances that make it viable to do so- if this were a more stable world, the ridiculous disparities amongst the sexes would itself become a threat to social stability and order. They need men to fight and women to breed; it's that simple at its basis, and they cook the books (as it were) to ensure that things work that way.
Why the misogyny? In part because the Inner Elite, being successors to the pre-Rifts global elites, see people first and foremost as tools--as assets--and not as fellow human beings. They look at women and see self-propelled baby manufacturing complexes; they view women that aren't breeding as being wrong, somehow, and a lot of their reactions to that perception of wrongness is meant to "fix" them (if possible) or recoup a loss (if not) by using them in some related capacity. The Inner Elite thinks in terms of math, of statistics, of profits/conquests and losses, and not in terms that would see the people under their power as equals, as fellows. They're not that much different than their predecessors in real history; the callbacks to Rome, Greece, China and other strongly patriarchal cultures is not accidental- it's, in many ways, an attempt to synthesize the successful (from their point of view) elements into a stronger whole- and they do this because they believe that this is natural law, and the women amongst their own class largely buy into it.
I'm trying my damnedest to create an evil society and culture that fits into the high concept of the States, and in my experience you have to get at elements like this to make it stick in play; the players (and their characters) may only see the tip of the iceberg, but there is a lot of depth supporting it that can make its presence felt if pushed.
The horror here is that, because the majority of Coalition subjects are totally ignorant of anything other than what Coalition propagandists tell them, all of this is normal to them. The women of the Coalition, by and large, don't think to question this social norm; in part because they lack the education needed to generate the critical thinking skills required to make that leap, and in part because--like all successful cults (and remember, the Coalition States runs off an Imperial Personality Cult)--they're kept far too busy working to think about much other than the here-and-now. The men of the Coalition don't do this because they are too busy fighting, training, recovering from same or in preparation for same to do much critical thought- even amongst the Outer Elite ranks. They aren't aware that they're repressed.; the Inner Elite successfully convinced the people that, as it were, the Devil doesn't exist.
Finally, the Inner Elite cheat like the rat bastards that they are. They know how past societies like theirs fell, they have a clear advantage in their telepathic powers, and they sure as Hell don't play fair. While they don't need to intervene often, they do need to keep their hands on the wheel (as it were) to keep this oppression machine going. It's why they are so focused on maintaining and sustaining perpetual warfare: it keeps the people focused on external threats, keeps the people away from looking at their leaders, and permits the government all of the power and privilege required to enforce their will. Hitler, Stalin, Napoleon, Mussolini, Tito, Pinochet and many other butchers would look on this regime and wonder at it- and, likely, feel at home.