Holden is seriously disturbed, made evident not just by the fact that he is telling the story from his bed in an asylum but also by his incredibly irrational and at times self-destructive behavior.
Yet the driving force behind much of his decision making is a sense of morals that is at times twisted but is always present. One of Holden's main concerns is the fact that the world around him appears to be losing its morality and the people are all phony, all incapable of following the moral code that Holden insists on placing on those around him. He is worried about even the smallest things like the foul language scrawled on the walls at the museum. The title of the book reflects his desire to be the catcher in the rye, to prevent children from running over the edge of the field and hurting themselves.
So despite his inability to recognize morality in others, like Mr. Antolini, somewhere inside Holden there is a deep sense of morals and a strong desire not just to follow them but to have others follow them as well.