Part of the reason Curley doesn't like Lennie is based in their physical stature. Curley is a little person (kind of suffers from a "Napoleon" syndrome), while Lennie is a big individual. When they shake hands, Curley's hands literally is swallowed and crushed by the grip of Lennie. Another reason Curley doesn't like Lennie is based on personality. Curley is angry, looking for a reason to fight. Perhaps because he is a little man, he has a natural antagonism that is predisposed to fight and this is enhanced with the fact that Lennie is so much bigger than he is. Lennie is so comfortable with his own sense of self and comfortable with his sense of his dreams and his happiness that this might instigate a bit of envy on the part of Curley, who seems incapable of being happy with anyone or anything. Whereas Lennie is steeped in his dreams and hopes, Curley is steeped in anger and resentment. This opposition outlines the difference between both, and explains the reason why Curley doesn't like Lennie. It also makes it very easy for Curley to organize the lynch mob against Lennie.
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.
Curley and Lennie are two people of two totally different personalities. Curley is always looking for a fight because he doesn't like "big men", but Lennie is unaware of this. Lennie lives in a dream world, he is only living because of the help of his companion, George Milton. When Lennie dies, the dream dies- as is the same with Curley's wife's death. She had life ambitions of which were unable to be fulfilled.
Curley doesn't like Lennie because he thinks that Lennie could be a threat to him. Curley is a very small guy and when he saw Lennie he did not like him because Lennie was bigger than him and curley did not like big men because they could be intimidating to him.