Why the hell would any girl ever enroll in this academy ever?
They receive an invitation, and because someone is making sure that the truth will not leak out, they only learn that it's not simply a prestigious academy when it's too late.
Better question: I probably missed this in the manga, but what is forcing the men to be a part of this system? What's making them act misogynistic towards the women?
Akane feared that rebelling against the system would make him unable to graduate. This is in addition to the fact that the school's Mega Corp backers will destroy the lives of anyone who defies them. These fears are probably shared by the rest of the men. Although it doesn't explain the more crueler actions done by the men since they could've left the girls alone.
What is the purpose of this school? Why create an atmosphere of extreme misogyny? If a couple of students decide to turn whistle blower after graduating, the school and the Mega Corp backing it are screwed.
The answers to all three of these questions are that the whole thing's heavily derived from Revolutionary Girl Utena which went very in-depth with its symbolism for systems of oppression. Of course, Utena examined how powerful male figures influence the less powerful by appearing to be admirable, while from what I hear Shitsurakuen is very binary about the whole thing. Still, there's your answer: it's just borrowed from Utena, which was very symbolic.