The book does not clearly say what the source of Curley's anger was. However, it does intimate a few things.
First, the book says that Curley was small in stature. It also says that because of this he hated big guys. Here is the text:
The swamper considered . . . . “Well . . . . tell you what. 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. You seen little guys like that, ain’t you? Always scrappy?”
The point is that Curley was insecure. So, he had to overcompensate when he felt threatened.
Second, Curley also felt entitled, because he was the boss's son. There are a few places in the book where this detail in mentioned. In light of this, we can assume that Curley felt that he could get away with certain things, because he had power on the ranch. So, he could get angry and get away with it. Who would stop him?
Third, Curley was also a fairly successful boxer. So, he was able to back up his anger with physical force at times.
Lastly, another details that emerges several times is that he felt insecure in his marriage. He was always looking for her and suspicious of other men. So, when things were not going well with his wife, it would turn into anger.
If we add all these details together, we see that he was insecure and entitled and this combination led to anger.