The conflict between Meg and Calvin is mainly a clash of personalities. Though incredibly bright, Meg doesn't do well at school; she just doesn't fit in. Calvin, on the other hand, is a very popular student and seems in his element both in class and on the basketball court.
Calvin also rubs up Meg the wrong way by spreading unfounded rumors about the Murry family. When he first meets them, he rudely says that Charles is "supposed to be a moron" and that Meg is "supposed to be dumb in school." If there's one thing we know about Meg, it's that she's fiercely protective of her family and its good name. But it's only when Calvin starts mouthing off about Dr. Murry's running off with another woman that Meg leaps to the defense of her family. It's fair to say that Calvin's got off on the wrong foot with Meg, and so it's no wonder she harbors such animosity towards him.