Holden Caulfield didn't run away to New York City because he was depressed; he did it because he's irresponsible. After being kicked out of Pencey Prep, he does not have an adult to guide his decisions. He knew that his parents will be angry about him being expelled so he wanted to avoid going home immediately. Holden acts like a typical unsupervised teenager by sneaking into bars, flirting with women, and spending a ton of money. Therefore, he is only being reckless because he has the freedom to.