Why did they have to move?

If you are referring to why Abilene Tucker and her father, Gideon, have to move, I can answer that question.
Both have to move to accommodate Gideon's job change. The text tells us that Gideon is hired for a summer railroad job in Iowa. Since he cannot not take his daughter with him, Gideon arranges for a preacher named Pastor Shady Howard to stand in as Abilene's guardian.
Abilene relates that she travels by train to meet the preacher in the town of Manifest and that she has little with her. Her most prized possession among her meager belongings is Gideon's compass.
Abilene's first meeting with Pastor Shady Howard is nothing like what she had envisioned. This is because Pastor Shady does not resemble the image of a typical preacher in Abilene's mind. He is dressed somewhat shabbily and exhibits strange behavior for a supposed man of the cloth. In time, Abilene comes to learn the truth about her father (his real name is Jinx) and how he was convinced that he would "jinx" her life if he didn't leave her.