An anti-hero is a protagonist who lacks heroic qualities such as courage, proactive decision-making abilities, and a strong sense of purpose. Holden tends to dream of acting like a hero in certain hypothetical situations, but when push comes to shove, Holden backs down, gets beat up, or avoids the altercation all together. For example, when he's walking back to his hotel from Ernie's in chapter 13, he imagines what he would have liked to have done if he had caught the guy who stole his gloves at Pencey. He prefaces his heroic adventure by first saying the following:
"I wished I knew who'd swiped my gloves at Pencey,, because my hands were freezing. Not that I'd have done much about it even if I had known. I'm one of these very yellow guys. I try not to show it, but I am" (88).
Once he admits that he is a coward, he continues on to describe what he would do if he were brave. He would confront the guy to his face and ask why he stole them. Then, when the guy denies knowing about the gloves, Holden says he would stand there and want to punch the guy. Rather than throw the first punch, Holden admits that he would probably just say something "very cutting and snotty, to rile him up" (89). Next, if the guy asked Holden if he was calling him a crook, then he would answer back that he didn't know, but the gloves were found in the guy's galoshes. In the end, Holden admits the following:
"Finally, though, I'd leave his room without even taking a sock at him. I'd probably go down to the can and sneak a cigarette and watch myself getting tough in the mirror" (89).
Holden is like this in many other situations throughout the story. He thinks big, but he doesn't act; he wants to be brave, but he backs down; and, he is still only searching for his purpose in life. He is probably incapable of committing to a purpose and sticking to it, even if he had one. Therefore, Holden proves to be one of the great anti-heroes in literature.
According to the definition of "antihero," as a character that is in many ways the antithesis of a hero, Holden certainly fits the bill. If you consider many of his interactions, he is incapable of reacting in the way that the audience would hope a hero would react. He cannot understand Mr. Antolini's willingness to help him and provide a helping hand. He fantasizes about being the "catcher in the rye" to save the little kids, but he is unable to follow through on almost any of his heroic ideas.
He is unable to defend Jane from Stradlater in a heroic way and ends up in a desultory fist fight with him instead.