One of the basic conflicts that emerges in the first chapter is the division between the Greasers and the Socs. For Ponyboy, he is caught in this conflict as the novel opens. He goes to the movies alone, an expression of a basic conflict between he and the world in which he is fundamentally different from others. On his way back and alone, he is confronted by the Socs. They assault him, abusing him. This conflict is representative of the larger issue in which the Socs feel they are able to intimidate and harass the Greasers. The antagonism between both groups represents one of the basic conflicts of the novel and is seen in the first chapter.
Another conflict is between how Ponyboy feels he will never be able to please Darry. There is a generational conflict that exists between how Ponyboy feels that no matter what he does he will never be able to reach the standards that Darry places on him. For his part, Darry is the "adult" of the family now and he believes in his role of taking care of the younger ones in the family, most notably Ponyboy. This conflict is emphasized at the end of the chapter when Ponyboy tries to convince himself that he does love Darry, which, of course, he does.