I'm wondering about the dichotomy between Kozue and Miki, whether it is really as... black and white, as it seems. This might devolve into incoherent rant, beware.
Kozue is presented as the one who wants to grow up and be an adult, and Miki as the naive, innocent one, who wants to remain a child. Kozue stopped playing the piano, Miki plays it obsessively trying to regain the feeling of his childhood. Kozue has sex with Touga in that same music room. When people first watch that, they interpret it as Kozue trying to push Miki away, but in actuality, going out with boys he would disapprove of is really just her way of trying to get her brother's attention. Kozue plays the piano behind Miki's back. Miki, in the end, is the one actually looking for a new shining thing, trying to find it with a new girl, while Kozue is the one who wants to have Miki back, and can't let go of him.
Kozue hurts the teacher who was creeping on Miki, but sees no problem in having sex with an adult herself. It's like she believes, that just like with his talent with the piano, that Miki has something precious about him worth protecting, something that she doesn't believe herself to have. Kozue saves the two baby birds. She claims she and her brother don't need parents, but that's the role they start playing for the little birds. Maybe she does want Miki to go and save her, wanted them to save each other, to be them against the world. Miki loses the duel when she kisses Anthy.
And Miki, he's supposed to be the naive one. The one who didn't realize the advances of his teacher, the wide eyed innocent one who doesn't know much about the "adult world". But is he? Is he really? Miki scolds Kozue for talking badly about their parents, says that they care. But, behind her back, he's upset about his father remarrying, even if he pretends to be okay with it when talking to the man. Behind her back, he's bitter, talking about how adults who tell you something is "for your own good" can't be trusted, about how he won't let some selfish adult use him. He deduces that Akio has "seduced" Touga. In the light novels, I've heard Miki and Touga have sex. It's unclear whether they did in the show, but Touga acts with him in a way that could very much be seen as flirty, and even called him "easy", so it's a possibility. The way Miki remembers the event that drove him and his sister apart has their father forcefully dragging a scared and pleading Kozue into a concert she didn't want to take part in.
So, are they really as oppositional as they may seem? Is Miki really naive, or is he similar to Utena, and he partially uses this act of naivety as a way to protect his mind from the ugly reality, especially from the parts he has little control over? Does Kozue really want the adult world, or is partaking in it just something she does in her search of regaining the childhood she lost? Could Miki and Kozue possibly just be two different presentations of the same thing?