Insanity is what is commonly referred to as a detachment from reality. A person who is psychologically deemed as "insane" acts and reacts out of nothing at all. Therefore, a person with a psychological profile of this nature is completely unaware of his or her role in society, their reason for action, or the existence of consequences.
This being said, it is close to impossible to relate these characteristics to Holden Caulfied. In fact, to call Holden "insane" would be to reduce his personality, his thinking processes, and his actions to mere instinct.
Therefore, to start off, Holden is NOT insane. Nor will he ever be anywhere near that.
What Holden suffers from is a clear case of PTSD, or Post Traumatic Stress Disorder. He is a "poster boy" for it. His trauma is caused by a combination of factors. However, the most important of those factors is the cruel death of his younger brother, Allie, due to Leukemia.
Allie's death, combined with Holden's natural growth processes and hormonal production as a teenager, makes his life quite hard to handle. It is very hard for Holden to understand why things are the way they are, however, he is clear in where he stands and has made a good argument against people whom he considers "phony". Contrastingly, "insane" individuals cannot develop arguments that they can substantiate.
What Holden has done is to create a reality which does not elude the situations that he has gone through. He is very aware of the death of Allie, and of his desire to protect the young and the innocent from the hard knocks of life.
If Holden is to be judged by his behaviors, the best bet would be to admit that his attitudes and opinions are nothing but protective mechanisms that would impair him from becoming too attached to people. As a result, he would not have to suffer as much as he did when Allie died. These are calculated and well-planned actions from the point of view of an immature kid. No insane person would be so analytical, methodological, nor precise in their choice of action.
There are many signs that show that Holden suffers an intense case of PTSD. They include his violent reaction to the death of his brother (when he broke all the windows in the garage), his deep connection with children, his desire to protect them, and his fixation with adults and fellow teenagers. Holden does resent the fact that he has not been able to overcome his brother's death. Therefore, it is hard for him to connect with his peers because they lack that one piece of reality that occurred only to him.
Conclusively, Holden does not have any type of insanity. Instead he suffers from a traumatic condition propelled by the death of his younger brother, and infused by his development as a teenager who has suffered a deep life-changing event.
It would depend on which stance you are taking on this argument. I on the other other hand, would argue that Holden is nowhere near insane. To me he didn't to be/showing signs of being insane. He actions are just extreme making it harder to understand him, but on the other hand he seems just like any other teenager out there. His only flaw is the fact that he hasnt learned to cope with events in his life, which explains why he acts the way he does.
I agree with the post above that mentions PTSD.
(Symptoms of PTSD: depression, sleeplessness, hypervigilance, weeping, negativity, self-isolation, attention deficit and trouble concentrating, exaggerated startle response, untrollable anger, recurrent invasive recollections of stressor events)
The book is full of examples.
First, there are two stressor events: Allie's death and the death of a classmate, Jame Castle, who leaped out a dorm window wearing the sweater Holden loaned him.
I was only thirteen, and they were going to have me psychoanalyzed and all, because I broke all the windows in the garage. I don't blame them. I really don't. I slept in the garage the night he died, and I broke all the goddam windows with my fist, just for the hell of it. I even tried to break all the windows on the station wagon we had that summer, but my hand was already broken and everything by that time...
Jame's Castle's death:
So Stabile, with about six other dirty bastards, went down to James Castle's room and went in and locked the goddam door and tried to make him take back what he said but he wouldn't do it. So they started in on him. I won't even tell you what they did to him--it's too repulsive--but he still wuldn't tke it back, old James Castle. ...a skinny little weak-looking guy, with wrists about as big as pencils. ...Finally, what he did, instead of taking back what he said, he jumped out the window. I was in the shower and all, and even I could hear hm land outside. ...I ran downstairs too, and there was old James Castle, laying right on the stone steps and all. He was dead, and his teeth, and blood, were all over the place, and nobody would even go near him."
On page three there's an example of attention deficit, when Holden leaves the equipment for the fencing team on the subway, resuliting in forfeiture of the match.
I was the goddam manager for the fencing team. Very big deal. We'd gone in to New York that morning for this fencing meet with McBurney School. Only, we didn't have the meet. I left all the foils and equipemnt and stuff on the goddam subway. It wasn't all my falult. I had to keep getting up to look at this map, so we'd know where to get otff. ...The whole team ostracized me the whole way back on the train.
In Chapter 6 there's an example of weeping:
"I just lay theere on the floor for a while, and kept calling him a moron sonuvabitch. I was so mad, I was practicaly bawling."
Also Chapter 6, Holden becomes enraged over the prospect of Stradlater "giving the time" to Jane:
Give her the time in Ed Banky's goddam car?" My voice was shaking something awful.
"What a thing to say. Want me to wash your mouth out with soap?"
"That's a professional secret, buddy."
This next part I don't remember so hot. All I know is I got up from the bed, like I was going down to the can or something, and then I tried to sock him, with all my might, right smack in the toothbrush, so it would split his goddam throat open. Only, I missed. ...Anyway, the next thing I knew I was on the godam floor and he was sitting on my chest,...
As a post above, says, Holden is a poster boy for PTSD.