First of all, the concept itself is clever. The series takes place at Ohtori Academy, a boarding school that some reviewers have described as a "nuthouse." It's also one extended metaphor for adolescence, and that becomes obvious from the beginning of the show. Once you realize that Utena takes place in a world with more hormones than logic, things like floating castles and swords magically appearing in people's chests seem strangely reasonable. It's an adolescent world; we rarely see adults, and the ones we do see are clearly unaware of what's going on among the students and have limited involvement. It's the students who run the show and who make the rules, which can change at any time. It's like a much prettier and highly sexualized version of Lord of the Flies.
I also liked that practically ever character in this series has some sort of backstory. What you see is never what you get, and just when you've written off Character X as an airhead or Character Y as a self-serving, manipulative bastard (and you are probably right to do so), you see a whole different side of him. It may not change your opinion, but it will throw you for a loop.
