The very first time he meets with Lennie, Curley immediately takes against him. As Slim points out to George, this is because Curley has a real problem with bigger guys. Curley's quite an aggressive character with a large chip on his shoulder, an ex-boxer no less, and like a lot of short men has a bit of a complex about his height. In addition, it's implied—but never explicitly spelled out—that Curley has a bit of a problem with satisfying his sultry, glamorous wife. So it's no wonder that Curley's always trying to prove his masculinity; and what better way to do that than pick a fight with someone much bigger than yourself?
Put all these factors together and you have an explanation as to why Curley hates Lennie so much.