The answer to this question is not a simple "he can read" because Dill is not a simple character in this story. Dill is based on Truman Capote who was a childhood friend of Harper Lee. He is not portrayed as "self-important" in the novel but rather a young boy who creates fantasies rather than deal with his life. His mother abandons him to live with relatives so she can pursue her own happiness. Dill has to have a make-believe life because his own is unbearable. He is a boy living in a world of adults and is suddenly given the gift of childhood friendship by Scout and Jem. He has to learn how to relate to someone his own age instead of standing out to adults. Harper Lee maintained a friendship with Truman Capote even while To Kill a Mockingbird was being published. She was recalling a fragile young man who arrived in a small town where everyone knew your business rather than a city where anonymity was the order of the day. The fact that Dill can read does not make him stand out anymore because Scout can do the same thing.
Because he can read. (He thinks this is a big deal because he's young until he finds out Scout [who is younger] can read.)
Dill feels very superior to the other children in Maycomb because he is "old" and he can read, although Scout can also.