You can find examples of Holden's mistrust and dislike of adults throughout the novel. For example, in the very beginning (and the first time we see him use the word "phony") he refers to the headmaster of Pencey as being a "phony slob." He describes a speech he heard at Pencey given by an undertaker in which the man tried to appear reverent and religious, mentioning that he "prayed to Jesus" while driving his car. This really set Holden off, and he concluded that the man was just trying to pray for more "stiffs" to increase his business. A total phony. His teacher, Mr. Spencer, tries to lecture him on doing better in school, but he dismisses this advice because as an adult, Mr. Spencer just does not understand.
When he goes to New York, he runs into his older brother's former girlfriend, who is a huge "phony." His favorite teacher, Mr. Antolini, gives Holden some really good advice, but unfortunately, Antolini sabatoges his own advice because while he is giving it, he is drinking heavily and getting drunk. Holden observes that the advice may not be valid when given by a drunk, and when he awakens to Mr. Antolini stroking his head, he automatically assumes it is an advance, and flees. This shows he does not trust adults because he automatically assumes the worst.
Finally, the only people that Holden feels comfortable around are children - his deceased brother Allie, and his little sister Phoebe. Everyone else is a phony.