Dill originally tells a wild story about why he ran away from home, but later explains that he just didn’t feel welcome since his mother remarried.
When Dill first tells Scout and his father, he says he doesn’t have one, but that he isn’t dead, a fact that confuses Scout. Jem tells her to drop the whole embarrassing topic. Family is a touchy subject with Dill. He also makes up wild stories about his father, including that he is a railroad president and is taller than Atticus. The truth is, Dill feels abandoned. He envies the relationship that Scout and Jem have with Atticus.
When his mother remarries, he has high hopes for having a real father. It does not work out as he hopes, so he leaves. At first, he makes up a real whopper of a story.
… having been bound in chains and left to die in the basement … by his new father, who disliked him, and secretly kept alive on raw field peas by a passing farmer who heard his cries for help … Dill worked himself free…. (Ch. 14)
He stole money from his mother’s purse and took the train to Maycomb. That was likely the only true part of the story!
The truth of why Dill ran away is less dramatic. Dill’s mother remarried, and his new father did not have time for him. His mother and father spent all of their time with each other, and he decided that they were better off without him. He felt frustrated, and missed his friends in Maycomb. His new father did not live up to his fantasies, and he lost his mother too. He later admits to Scout that the story is not true, and his father is not as “hateful” as his colorful story. He said they would spend time together, and then they didn’t.
"That wasn't it, he- they just wasn't interested in me."
… "How come?"
"Well, they stayed gone all the time, and when they were home, even, they'd get off in a room by themselves." (Ch. 14)
Dill’s family is really Jem and Scout, and his aunt. He relies on them for a sense of stability. His mother seems to be flighty at best. His stepfather made promises he did not keep. It makes sense that Dill was disappointed. In the Finch household he saw something he envied—a father-child relationship.
Dill perceived himself to be a victim of negligence. He felt he was not given the attention and care every child is entitled to receive from his/her parents. According to Dill, his Mom and Stepdad didn't want him anymore. As a result, he didn't want to stay with them.