Some conflicts in The Outsiders are man vs. man, man vs. society and man vs. self.
An example of a man vs. man conflict in the story is the greasers vs. the Socs. This is the larger conflict, which can be broken down into specific conflicts between characters. One such conflict occurs in the fight between Johnny and Bob in the park during the rumble that resulted in Bob’s death. Ponyboy explains that the fighting between the greasers and the Socs often occurs just because it has been perpetuated from one jumping or rumble to the next, or because of the general class differences between the two, and not for any specific reason. This is evident in the way that Bob attacks Ponyboy and Johnny in the park.
Bob shook his head, smiling slowly. "You could use a bath, greaser. And a good working over. And we've got all night to do it. Give the kid a bath, David." (Ch. 4)
The conflict between the greasers and the Socs led directly to the conflict between Bob and Johnny, which led to Bob’s death. Johnny was just defending himself. He did not mean to kill Bob, and his killing Bob is what caused him to flee. All because greasers simply cannot get along with Socs.
This brings us to the second conflict, man vs. society. This occurs on a more global level. It involves a conflict with the world around a character. It is the problem that created the greasers and the Socs: class differences. There is a huge socioeconomic difference between the two classes. Pony explains the difference between the two groups in terms of social class.
We're poorer than the Socs and the middle class. I reckon we're wilder, too. Not like the Socs, who jump greasers and wreck houses and throw beer blasts for kicks… (Ch. 1)
It is this difference in social class that leads to the man vs. society conflict that the greasers have. Some of the greasers have a chip on their shoulder that causes them to attack the world, but many of them are just fighting to survive. While the Socs can leave once they are done getting their kicks, the greasers are trapped. They are in an endless cycle of poverty and violence, targeted by Socs and having fewer opportunities.
Finally, there is the man vs. self conflict. This kind of conflict involves a fear, a choice, or a decision. This is faced by Ponyboy, who is more thoughtful and insightful than most of the young people in the book. He wants to end the cycle of poverty by getting an education. However, he gets caught up in the incident at the park and has to go on the run. He wants to support Johnny, and his brothers, and the other greasers. He is proud of who he is, but he also does not want this life. He does not really want to be a greaser. It is a decision and a conflict that weighs on him.