One of the main ways that Salinger helps the reader to understand Holden's instability is through contrasting his thoughts and his actions. The way that Holden talks about the world and the way that he acts within it are completely different and difficult to understand.
When Holden decides to leave school, with the understanding that he'd likely get kicked out anyway, he goes to see Mr. Spencer and it is clear that he felt some sort of bond with the old man and the old man cared for him. Yet Holden discusses how much he is disgusted by the old man.
As the novel progresses, Holden's grip on reality begins to falter even more. He fantasizes about getting shot, tries to get Sally to run away with him even though it isn't even a remote possibility, and hides from his parents while also trying to sleep with a prostitute and then realizing that all he really wants is someone to talk to.