When Curley attacks Lennie and he fights back at George's direction and crushes Curley's hand, it is Slim who convinces Curley not to turn Lennie in. Slim tells him to say he got his hand stuck in a machine, and if he doesn't, he and the men will tell what really happened and Curley will be laughed at by everyone, something he fears a great deal.
Well that is easy. Curly is set out to be the Macho Antogonist in the novel. It would be a slam to his identity if he was beat up by a mentally challanged man. Not to mention that Lennie is a mere ranch hand he is supposed to be inferior to Curly. Curly is supposed to demand respect from the lower level help and he cannot do this if they no that he was put down by a helper.