In chapter 12, what is the best way to describe the loneliness and depression that Holden is going through?

Holden's loneliness and depression is expressed in this chapter through his question of the cab driver about where the Central Park ducks go when the weather gets cold. Holden hopes the cab driver knows where the ducks go, but he is not interested in talking to him about this topic, instead he yells at him, which only makes Holden feel small and insignificant no one will answer his question.

"The cab driver, Horwitz, is impatient with Holden, and always sounds angry when he is talking. Holden asks him where the ducks go in the winter. Horwitz answers in an irascible manner that he does not know, but then begins talking about the fish in the lake."

 This inquiry is really very symbolic of Holden's whole problem.  His question is not so much about the ducks in particular, but really references his desperate need to understand the unpredictability of life and the uncertainty of death.  Holden harbors deep unreleased feelings of grief and sadness over the untimely death of his younger brother Allie.  

Because of Allie's death, 3 years earlier, Holden has been unable to concentrate on school, find meaning in socializing with his peers and unable to make friends.  

So in Chapter 12 while he is in NYC, he is trying to find someone to connect with, yet he can't go home.  He wants to unburden himself of his current anxiety, getting kicked out of another school, onto someone who will understand and sympathize with him.  He keeps looking for a shoulder to cry on, but keeps coming up with nothing but resistant, uninterested people, who Holden views as phonies.  This realization only deepens his loneliness and feelings of isolation.

He goes to Ernie's to hear him play the piano, at the same time insulting him about his phoniness, complimenting him for his skill at the piano.  Ernie's a big snob according to Holden.

First Holden observes that he was:

"surrounded by jerks.  I'm not kidding.  At this other tiny table, right my left was this funny-looking guy and this funny looking girl." (Salinger)

Then Holden finds himself face to face with his brother D.B.'s old girlfriend Lillian Simmons accompanied by a Navy guy.  The thought of sitting with them and making small talk makes Holden physically sick.  He was very upset that he had no choice but to leave Ernie's in order to get away from him.

"But I certainly wasn't going to sit down at a table with old Lilliann Simmons and that Navy guy and be bored to death.  So I left.  it make me mad, though, when I was getting my coat.  People are always running things for you." (Salinger)

At the end of this chapter illustrates just how Holden feels about his life.  He does not feel like he is in control of his own life, he feels like he is a pawn of his parents, who, for Holden are real big phonies who do not understand him.