In chapter two, George and Lennie meet Curley for the first time. His personality is angry and arrogant, and he seems to be looking for a fight. He has a chip on his shoulder, which means something is always eating at him; probably a sense of inferiority from being short. He also, however, has outward confidence from being the boss's son: the deck is stacked in his favor, and he knows he can bully the ranch hands, who can't afford to fight back if they want to keep their jobs.
When Curley meets Lennie and George for the first time, he shows his arrogance or sense of superiority. He asks them questions, and when George answers for Lennie, who is upset by Curley, Curley responds arrogantly:
By Christ, he’s gotta talk when he’s spoke to. What the hell are you gettin’ into it for?
Curley shows his arrogance by insisting that Lennie's "gotta" answer when Curley speaks to him, as if Curley is a king. This is not a kind way to treat a new employee. Instead, Curley rubs his employees' inferiority into their faces by lording it over them.
Curley also responds angrily when he meets the two new ranch hands. After having hardly spoken to them:
His arms gradually bent at the elbows and his hands closed into fists. He stiffened and went into a slight crouch. His glance was at once calculating and pugnacious.
This shows that Curley is not only angry, but a person who looks for a fist fight. We learn a little bit later that he is a lightweight boxer, which is no doubt why he went into a crouch when he felt threatened by George and Lennie. Candy tells them:
He done quite a bit in the ring. He’s a lightweight, and he’s handy.
Candy also explains why he thinks Curley has a chip on his shoulder:
Curley’s like alot of little guys. He hates big guys. He’s alla time picking scraps with big guys. Kind of like he’s mad at ‘em because he ain’t a big guy.
George becomes worried that Curley is a mean bully who is going to cause trouble for Lennie. He warns Lennie repeatedly to stay away from him. George says of Curley: "I don’t like mean little guys.”
Candy also tells them that Curley just got married and that is making him worse than ever: it seems he wants to prove himself to his wife.
George says to Lennie a little later:
Look, Lennie! This here ain’t no setup. I’m scared. You gonna have trouble with that Curley guy. I seen that kind before. He was kinda feelin’ you out. He figures he’s got you scared and he’s gonna take a sock at you the first chance he gets.
We can tell from chapter two that Curley is a mean, arrogant bully with an inferiority complex who will probably make trouble for George and Lennie if he gets the chance.