The Greasers and the Socs dislike each other, because they do not understand each other. There is a vast socioeconomic divide that exists between the two groups. The Greasers hate the Socs, because the Greasers believe that the Socs have it easy with all of their money and privilege. The Socs hate the Greasers, because they are easy targets to hate. The Greasers are poor and powerless, so the Socs feel that they are entitled to beat upon the low life Greasers. Each group cannot seem to relate at all to the other group, so there is fear and hatred there. People tend to dislike what they do not understand. That's why I disliked college philosophy. I just flat out didn't understand any of it; therefore, I told everybody that it was the worst class ever. Socs and Greasers don't understand each other, so dislike follows shortly after.
What neither group understands though is that they are more alike than different. Cherry understands it, and she understands it early in the novel. It's why she tells Ponyboy that "things are rough all over" in chapter 2.
Late in the novel Randy comes to talk to Ponyboy. At the end of the conversation, both boys seem to genuinely understand where the other guy is coming from. Because of that, both boys leave the encounter with mutual respect for each other, not dislike.
"Thanks, grease," he said, trying to grin. Then he stopped. "I didn't mean that. I meant, thanks, kid."
"My name's Ponyboy," I said. "Nice talkin' to you, Randy."
I walked over to Two-Bit, and Randy honked for his friends to come and get into the car.
"What'd he want?" Two-Bit asked. "What'd Mr. Super-Soc have to say?"
"He ain't a Soc," I said, "he's just a guy. He just wanted to talk."
Notice that once understanding between Pony and Randy happened, all negative slang and name calling dropped out. No longer was there a faceless group to dislike. Now there was another person, with problems of his own.