The rift between the Socs and the greasers is a socio-economic one. The Socs are the rich, pampered kids; they dislike the greasers based on general distrust of their 'hood'-like appearance. In the Socs' minds, the greasers are nothing more than poor trouble-makers and hoodlums. On the other hand, the greasers dislike the Socs because they feel like the Socs have all the advantages and are spoiled, rich kids. Ponyboy observes that the Socs have all the breaks-- it is hard to feel sorry for someone who has a 'tuff' mustang.
Particularly, Ponyboy's greaser gang holds a particular grudge toward the Socs in their towns after the Socs mugged and severely beat Johnny Cade. Their treatment of him intensified the conflict between the two gangs.
One day Johnny kills a Soc.
It's because they were different from each other.