I think Kozue Kaoru is kind of a hard character for a lot of people to get because her actions seem to contradict themselves. In episode 15 she is very hostile to Anthy, I've even seen people call her a "yandere" here. But in episode 26 she seems to encourage Miki to "go for it" so to speak, if that's what he wants. In episode 17 during the badminton scene, we get a shot of Kozue after Miki seems to confess having a crush on Utena, and she seems totally unbothered. A direct contrast here is in Shiori, who in a similar shot looks, in my estimation, pissed off.
Maybe some people interpret her character as changing or growing between the two Kozue-focused episodes, but I don't really think that's the case. There's no reason for that to have happened off-screen. It's more that I think her feelings towards Miki himself are a bit contradictory. On the one hand, she seems as obsessed with his purity as he is with her's, secretly protecting him from the handsy piano teacher, and claiming to not tolerate anyone who would hurt Miki. On the other hand, she seems completely frustrated with him for refusing to grow up, for fixating on childhood and rejecting adults, & for not taking power. And I think "adulthood" for Kozue is synonymous with having been in abusive situations, in sexual situations, not being naive to those things. (In the same way that the knowledge that Saionji senses Touga has but he doesn't is also the experience of being sexually abused). And from that springs the contradictory impulse, both wanting to protect Miki from that, but perhaps feeling resentment, or exasperation that Miki doesn't truly know her, when he hasn't had the same experiences.
And I think the whole “twin thing” plays into that too. Like twins are “meant to be” the same person. but Miki and Kozue upon their separation as children were differentiated from each other. and Kozue believes/lives in a world where "purity" can be lost, but not regained. so to become "like" each other again, to her there seems to be only one direction in which that can happen. And in the scenes immediately after Miki's car ride, both Kozue and Miki act the most "in sync" as twins (to the point that I think it even creeps Utena out a little when they both stare at her like that...) But of course as much as a part of Kozue wants that, a part of her doesn't want that either, because it's awful. So her actions can seem quite nonsensical and inconsistent.
