My interpretation of Miki’s character is that he represents (among other things, of course; nothing in RGU is black and white) society’s obsession with the “purity” of woman.
Content Warning: Mentions of incest and sexual abuse
So, Miki wants to preserve things he finds beautiful, “shining”, but never really goes into what that means. Well, what he found “shining” was his childhood memories of Kozue, before she changed. This change was spurred by the implied sexual abuse of her by their father, which led to her becoming hypersexual and being unable to enjoy the innocent activities of their childhood any longer. In a sense, she was forced to grow up extremely quickly, while Miki stayed trapped in the idealistic version of their childhood. To Miki, her becoming ‘impure’ meant that she was no longer ‘shining’. He’s also shown to be extremely affected by displays of sexuality towards Kozue or Anthy; Touga manipulates Miki through a relationship with Kozue. He loses his second duel when Kozue kisses Anthy. Touga all but outright tells Miki that the only way he can preserve the purity of women is to own them. Miki wants things to remain as they did in his childhood; he wants Kozue to remain as her child self. He also is shown to value femininity in Anthy. These two things reflect the infantilization and feminine ideal that go hand-in-hand with the standards for women’s purity.
This also ties into how he objectifies Anthy and Kozue. Obsession with purity reduces women to objects who's only value is tied to sex. Miki's burgeoning misogyny might not be as blatant as, say, Saionji or Touga's, but it is still very much present and represents, like them, yet another facet of patriarchal control.
