Curley has a complex about being small and compensates by playing the bully. To "strut his stuff" he has taken up boxing and just looks for an occasion to show what he can do.
Lennie Small (his last name, by the way) might be retarded, but he has the physique of Atlas. Curley is intellectually superior and quicker, which is enough reason for him to take Lennie on. When he sees Lennie smiling in a rather goofy way while the ranch hands are discussing his wife, Curley thinks he is the target of a crude joke and aggresses him. He underestimates Lennie's strength and when Lennie breaks his hand (in self-defense), the other ranch hands have to pry him loose.
Curley is by far the most antipathetic character in this story. When the manhunt, led by Curley, is out to get Lennie (who has accidentally strangled Curley's wife to death in the barn), just the thought of Lennie being at the mercy of such a beast makes George shoot him instead.