Your right, my teacher didn't tell us this interpretation in my school. The book makes more sense now.
Read the first page: "Besides, I'm not going to tell you my whole goddam [sic] autobiography or anything. I'll just tell you about this madman stuff that happened to me around last Christmas just before I got pretty run-down and had to come out here and take it easy."
Holden is in a mental hospital. This is confirmed on the last page [approx.] of the book.
"I could probably tell you what I did after I went home, and how I got sick and all, and what school I'm supposed to go to next fall, after I get out of here."
From that, Holden is in the hospital. The last line of the book says, "Don't ever tell anybody anything. If you do, you start missing everybody."
From what I remember, this means that Holden made up all of those stories. His family realized he was crazy because they know none of those things actually happened, put him in the hospital, and now he doesn't get to see his family or friends very often.
Of course, the fun thing about fiction that also doesn't get said enough is that the debating over what happened is part of the fun. I had one teacher who would present these analyses like they were hard fact, when in reality the only fact is what the author gives you, and the analyses can be debated with that in mind.