Why did Holden's parents want to have him psychoanalyzed?

Holden's parents wanted to have Holden psychoanalyzed because he broke all of the windows in the garage with his fist.
Holden even tried to break the windows on the car with his fists that summer as well. At that point, though, his hand was so broken and messed up that he couldn't do it. Holden tells readers that he broke all of those windows "just for the hell of it." That may be what Holden tells readers, but that is not the reason that he broke all of those windows.
Holden broke all of those windows because he was angry and sad at the fact that his younger brother, Allie, had died. Holden idealizes Allie. Allie was basically the perfect child according to Holden. Everybody liked Allie. He was friendly, intelligent, and kind to people.

You'd have liked him. He was two years younger than I was, but he was about fifty times as intelligent. He was terrifically intelligent. His teachers were always writing letters to my mother, telling her what a pleasure it was having a boy like Allie in their class. And they weren't just shooting the crap. They really meant it. But it wasn't just that he was the most intelligent member in the family. He was also the nicest, in lots of ways.

Unfortunately, leukemia killed Allie at the age of eleven. Holden broke all of those windows because he was angry at the injustice of Allie having to die. Holden's parents just didn't understand that for some reason, so they wanted to have him psychoanalyzed by a professional.