Darry challenges Ponyboy to do better, but it makes him mad and annoyed of the constant discipline and control of his life. Ponyboy gets annoyed and feels like he is a curse or burden to Darry, but what he doesn't really realize is Darry really cares for him and wants him to succeed. When Darry slaps Ponyboy because he came home super late, his strict actions and fierce anger when cause Ponyboy to be very sad and hurt, so he ran away. Dally was just worried and scared for Ponyboy.
Every day he needs to avoid and watch out for Soc's so he won't get Jumped. This conflict makes him mad because he feels pressured and unsafe. Ponyboys can't solve this conflict because Ponyboy depends on the Greasers, but being a Greaser means you fight Socs. He cannot control that he is poor and lives on the bad side of town, and the conflict doesn't end after the big rumble, and it will never stop. Ponyboy needs to act tough and mean when really he is nice and non-violent.
Darry is always criticizing and strict to Ponyboy, so Ponyboy is annoyed with Darry. This causes Ponyboy to feel like Darry doesn't like him so he is sullen and annoyed. Ponyboy can control this conflict if he thought more and didn't annoy Darry, but that is very hard for him. After a big fight, the conflict is resolved when the brothers realize their fighting puts a lot of pressure on Soda, and they never listen to his problems, so they decide to be more considerate of each other and stick together.