In The Catcher in the Rye, it's fair to say that Holden's relationship with Phoebe is the only close one that he has. Whether it's his parents, teachers, or the adults that he happens to meet on a daily basis, Holden is chronically incapable of establishing close connections with anyone else.
To a large extent, this is because Phoebe isn't a part of the adult world that Holden positively loathes and that he's never really understood. For Holden, this is a sham world, a world full of phonies. But Phoebe's not like that; she's still young and innocent, the kind of child that Holden fantasizes about preventing falling off a cliff. For good measure, she seems to understand Holden in a way that no one else ever could.
One could also say that Holden's closeness to Phoebe derives to a considerable extent from the painful loss of his late brother, Allie, who died tragically young of leukemia. Having lost one sibling, Holden doesn't really want to lose another. And so he remains fiercely protective of Phoebe, even though he eventually realizes, as he watches her on the carousel at the end of the story, that he has to let go and let her live her own life.