how is phoebe able to be so insightful?

This is a great explanation from GradeSaver for what you need,

Phoebe, Holden's nine-year-old younger sister, is more mature and intelligent than her age implies. She realizes the extent of her brother's misanthropy and unhappiness. Holden appreciates every minute detail of Phoebe's existence, it appears, including her stories about "Hazle Weatherfield, Girl Detective." Holden treats Phoebe with more respect and kindness than he treats any other character in the story. Phoebe, for her part, recognizes how tenuous Holden's grasp on reality is. Unlike her parents, she knows he is struggling, and she simply wants to be there for him. In the end, it is her willingness to go to the ends of the earth with him that wakes Holden up to the impossibility of his self-destructive impulses. He succumbs to this reality because he cannot bear to see Phoebe suffer.