In A Thousand Spledid Suns, Laila feels a strong attachment to her father primarily because he respects women and supports her education. Her father is an academic himself, so he raised Laila with the belief that education for all is important. At the time the story is set, there are still people in Afghanistan who believe that women should not be educated--this dynamic is shown in the experience of the novel's other major character Mariam. Laila's family is considered fairly progressive, so she was sure to be educated.
In addition to liking her father's support of her education, Laila also feels attached to her father because her relationship with her mother is a bit distant. Laila's brothers are away at war, and the mother is almost consumed with thoughts of them. She is harsh with both Laila and the father, so the two commiserate at home.