What are the unrealistic aspects of Holden's desire to be a catcher?
The unrealistic aspect may be that he thinks that he would have the power, an unrealistic power, to save EVERY child from danger. He gives a lot of power to the idea that it IS possible to collectively save children from danger (or in his case, from "falling off some crazy cliff") by only one course of action, and he is even more unrealistic in thinking that this is a possibility that he has an option to fulfill that duty.
Holden was terrified of the dangers of adulthood and cherished children for their innocence and their honesty. This idea to become a catcher in the rye was an unrealistic view at protecting children. The unfortunate truth is that nobody is really safe from the evils of the world, and there is no catcher in the rye to help children be more protected.