Kozue is Miki's identical twin sister. The two are extremely close, since they've been living on their own for a while. Their parents are divorced, but they don't care too much about their parents' affairs. As Kozue said, they're wild animals. They don't need parents.

The story behind the two (as if you never heard it before) is that when they were little, they used to play the piano together in the garden outside their house. Miki was an excellent player, and his skill covered up Kozue's blunders, but he never noticed it. The pair composed a song called the Sunlit Garden, and became so good at playing it that neighbors and people from far away would come to the garden to listen to them play.
But then I destroyed it! I destroyed it with my own hands!
Miki booked the two to play at a concert hall, but the night before he came down with a cold and couldn't play. Kozue was carried off to play in the concert hall anyway, but once on stage, she ran off crying and hid for the rest of the night. This was the spark that caused the two to divide.

Since then they were never the same. Miki continued to play the piano, but without his heart in it. He became more and more skilled, but the only song that meant anything to him was the Sunlit Garden (which is why Anthy playing it that one time had such a big impact). Kozue, on the other hand, hardly ever touched the piano again (most places say she never did, but there are a few episodes where you see her playing). Instead, she turned into a player, using up boys to try to fill her heart up in the spot where Miki used to be. She's isn't a slut, she isn't used by boys, she uses boys for her own purpose. And as insult to injury, she purposefully dates boys she knows Miki doesn't like. This keeps him interested in here, if not in an outwardly loving manner then to protect her. Miki trys desperately to regain the love that they had, but is never sucessful in his mind.

So even though it appears the twins don't care much for each other anymore, they really do. Scenes from their bedroom in their dorm, and how Miki always made an extra milkshake for her suggest that they still really need each other. They're just playing stunts on each other: Kozue is constantly trying to get him back for "betraying her", and Miki knows this and is rude to her when she does.

Well, I'm sorry if that was a big jumbled mess. I'll organize all of it later, I promise :)