The Socs and greasers fight because they are...
The conflict between the greasers and Socs cannot be easily resolved.
The conflict between the Socs and the greasers is not actually resolved in The Outsiders, but Bob’s death helps resolve it because some of them no longer want to fight.
The Socs and greasers fight because they are in opposite social classes. The Socs are rich, and the greasers are poor. They are caught up in a cycle of violence, and as long as they are fighting, one fight will result in retaliation which will cause another fight.
Most of the violence between the two groups happens for no reason. Although the book is from the point of view of a greaser, Ponyboy, and is biased it does seem as if the Socs are initiating a lot of violence because they have less to lose. They are rich and it is fun for them.
The greasers are delinquents, real criminals, and the Socs are just kids messing around. They have futures, and will grow up and go off to college, not jail.
Greasers can't walk alone too much or they'll get jumped, or someone will come by and scream "Greaser!" at them, which doesn't make you feel too hot, if you know what I mean. We get jumped by the Socs. (Ch. 1)
Usually it happens like this. A group will just attack one person walking alone, who is vulnerable. Sometimes a group will attack another group, which is known as a rumble. This will often involve weapons, usually knives, “chains and heaters and pool sticks” (Ch. 2), although not always.
The crux of the issue happens when Ponyboy and Johnny are in a park and get attacked by a group of Socs. Johnny has been jumped before, and it has made him very jumpy. He tries to defend Ponyby, because one of the Socs is trying to drown him in a fountain. Johnny has a knife. This incident becomes serious, and Bob is killed. Johnny and Ponyboy go on the run. Eventually, Johnny dies as well in an accident.
After this, although there is another rumble, not all of the Socs are interested. Some of them are starting to second guess the entire cycle of violence. An example of this is Randy. He tells Ponyboy that he does not want to go to the rumble held to get revenge for Johnny’s death.
"I'm sick of all this. Sick and tired. Bob was a good guy. He was the best buddy a guy ever had. I mean, he was a good fighter and tuff and everything, but he was a real person too. You dig?" (Ch. 7)
This is an example of the conflict between the Socs and the greasers beginning to resolve. Some of the Socs at least do not want to keep fighting. Not all of them feel like Randy, but as time goes on, perhaps the tide will turn. Ponyboy does not want to fight either. He never did.
It is difficult not to belong to a gang when you are born into it, because everyone in your neighborhood is. The lesson here is that the conflict between the Socs and the greasers is societal and systematic. It will not be easily resolved. Bob’s death was a wake-up call, but this is not a problem that will go away overnight.