In The Outsiders, Ponyboy says "I'd rather have anybody's hate than their pity" because pity makes him feel weak and inferior, reduced to a poor greaser who needs sympathy.
Hate is painful, but it fits the world Ponyboy already knows. The Socs jump greasers, call them names, and treat them as enemies. Bob openly insults greasers as "White trash with long hair," and Ponyboy fires back with "White trash with Mustangs and madras." In that kind of exchange, Ponyboy can answer back. He can defend his pride and meet the Socs as an opponent.
Pity feels different to him because it comes from above. Ponyboy is deeply aware that Socs have money, cars, safety, and social respect, while greasers are judged by their clothes, hair, and neighborhood. When he thinks, "It wasn't fair for the Socs to have everything. We were as good as they were; it wasn't our fault we were greasers," his anger comes from wanting recognition rather than charity. Pity would confirm the very class divide he resents.
Cherry's lesson to Ponyboy, that "things are rough all over," is what pushes Ponyboy to see that both Socs and greasers are human. Later, Randy, a Soc, similarly begins to see Ponyboy as a person rather than as a greaser.
Ponyboy’s resistance to pity is tied to his need for dignity. He wants people to stop judging boys like him by their appearance, class, or reputation, and to instead see them as full people capable of complex emotions.