When the Phantom, Christine, and Raoul are in the Phantom's catacombs, Christine tells the Phantom that she hates him, then she kisses him. And when she and Raoul are leaving she looks back at the Phantom and sings. Why did she say she hated him?

It's very easy if you look at it in Christine's point of view. She loves Raoul very much but, the phantom tries to strangle Raoul, that is the reason why Christine tells him she hates him. You better keep thinking of the line which Christine said, "The tears of mine which were shed of your dark past turns to tears of Hate!"