As the previous poster mentioned, Holden has a very hard time accepting the truth from anyone else, but he also gives indications that he is trying to express the truth of his situation without actually being able to do so. Perhaps it is this constant disappointment in the inability of others to tell the truth that drives him to tell the story the way he does rather than simply saying right out that he is in a mental institution and has had a breakdown.
Instead he tells his story in a retrospective fashion without speculating as to why he is now in a mental institution and allowing the reader to judge for themselves whether the truth is coming out or not.
The other way that Holden tells the truth is that he places all the blame for any of his inconsistency and problems at other people's feet. He doesn't diagnose his own problem, again allowing the reader to make the truth out in whichever way they choose.