I think the fact that Holden is finally talking to someone after these events happened shows that he has changed, thus making him a dynamic character. In the beginning of the book, he says how he doesn't want to talk about his family and childhood but then further into the book you see he talks a lot about his past and his siblings.
I think the reason he might come off as a static character is because he is he is recounting these events to the therapist. These events happened in the past year. Now he is 17 and finally getting the help he spent the past year looking for. Thus, making him a dynamic character. Dynamic characters experience some major event(s) that ultimately change(s) them. Holden has so many of these!!! Starting off when his brother died when he was 12 which resulted in him punching the garage windows; when he watches his classmate kill himself while he was in the shower and he is traumatized by the goriness of James Castle’s remains splattered outside; and when he was molested as a kid making him both crave and hate being intimate/touched. All of these things make us understand why he is the way he is. Although these events do not excuse his behaviors, it does clear some things up and makes us feel sympathy for this damaged boy.
Going back to how he says “What I felt like, though, was committing suicide. I felt like jumping out the window. I probably would’ve done it, too, if I’d been sure somebody’d cover me up as soon as I landed. I didn’t want a bunch of stupid rubbernecks looking at me when I was all gory.” It is an oddly specific thing to say about such a serious matter. Then you realize it is much more than Holden not wanting anyone to see him or the effect it would have on his mother but it's because once he dies everything is out of his control. He likes things to stay as they are. He doesn't like change. This evident throughout the story. After all everything changed after Allie died. He says because a kid he knew did that. Holden remembers how that happened. He heard him hit the ground. Implicitly, he doesn't want to execute that plan as he fears it will traumatize anyone that sees him doing it or the aftermath of it. Someone else could be in the bathroom and they could happen to look out their window at the same time Holden is falling to his doom. He also doesn't realize how the person covering him up would still see him. Going back to the Secret Goldfish, he wants to kill himself but doesn't really want anyone to see it. It's inevitable though. The first person he tells someone about this event is his sister. Now he is telling that to the psychoanalyst.
Also we realize why he doesn't see the purpose of going to a good college and going into a nice profession, why he is basically throwing all that away. It’s because he just want to be the catcher in the rye. “I keep picturing all these little kids playing some game in this big field of rye and all. Thousands of little kids, and nobody’s around - nobody big, I mean - except me. And I’m standing on the edge of some crazy cliff. What I have to do, I have to catch everybody if they start to go off the cliff - I mean if they’re running and they don't look where they’re going I have to come out from somewhere and catch them.”
He just wants to protect little innocent kids from going off the rails, jumping off the cliff to their doom. He doesn't want anything to hurt them like he has been hurt. Childhood is an important factor to Holden. He doesn't want to taint it even though it is inevitable and has already happened to him. Because these events have such a strong impact on him, it has affected his future and his goals.
He is in denial after going to the museum as he keeps saying how he doesn't know why he hasn’t come across a single duck while in the park. Yeah the underlying point is that Holden doesn't know where to go from here. He has no sense of direction unlike ducks. Birds are typically a symbol for freedom as they can fly and live both on land and water so they have so many places to go. They know to fly south for the winter. So it is wintertime and Holden is looking for the ducks. He is looking for something he is never going to find to distract himself from reality as well as a way to indirectly ask for help. He doesn't know if someone is going to come and help him find his way because he definitely can't do it on his own. He spends this whole journey trying to figure out where the ducks go during the winter when he knows very well that birds fly south for the winter!!!!! “There were even more upstairs with deer inside them drinking at water holes, and the birds flying south for the winter.” He clearly knows more than he is letting on.
Another example is when Holden is talking about the Egyptians to the boys he meets. He mostly knows what he is saying showing that he purposefully wrote a trash assignment for Mr. Spencer. An important tradition they did in Ancient Egypt was preserve their beloved and praised rulers after they died with a strong aspiration for a happy afterlife. Holden mentions how modern science wonders about the secret chemical the Egyptians used to preserve the ones that died. He thinks a lot about that because he is trying to preserve Allie even though he is never going to come back. In fact he is trying to preserve his childhood and childhood friends just like one would remember their rulers. He mentions how he just really likes how everything is always the same way as the last time he was there. Again, he doesn't like change. He likes knowing it is certain that nothing will be different. “The best thing, though, in that museum was that everything always stayed right where it was. Nobody’d move. You could go there a hundred thousand times, and that eskimo would still be just finished catching those two fish..” He refuses to admit how you would only change physically and not mentally. He says he just can’t explain it and maybe he really can’t. But he knows. This is evident when he says “Then a funny thing happened. When I got to the museum, all of a sudden I wouldn’t have gone inside for a million bucks.” He doesn't want to go in because he is afraid he is going to be different, the kind of different he says he can’t explain. He would always go there as a kid and now he’s 16 and doesn't want to go in and change anything. He is afraid of that taint. When you think about it, a museum has a lot of glass cases that show you things people have discovered over time. This one is historical and Holden likes to reminisce the past a lot and just stay on the past. The glass cases go back to the Secret Goldfish. Nothing is hidden behind a glass case.
I think when Holden finally breaks down it is significant to him realizing he needs help. First his record breaks. He loves this song because it reminds him of being young like the girl in the song and it reminds him of Phoebe. He got it for Phoebe. But then it breaks! Just like his childhood was damaged and he has been trying to pick up the pieces since. He is a broken record!!!!! He takes the pieces with him even though they are useless but they are still important for him. Then he starts thinking about Phoebe and she is the only one that can get through to him. She ends up convincing him to come home. She also happily accepts Holden’s gift, despite it being useless. In the carousel scene, Phoebe doesn't want Holden to keep going in these circles because he is ending up in the same place. It is the same story over and over again. She is worried about him and she wants him to come home and solve his issues. Again, Holden says “that’s one nice thing about carousels, they always play the same song.” at first you think he really isn’t going to change and how this would only make him a static character but then he says “The thing with kids is, if they want to grab for the gold ring, you have to let them do it, and not saying anything. If they fall off, they fall off…” thus he realizes that childhood is going to end no matter what. You cannot always be there to protect them and bad things are bound to happen. So he gives in and decides to go home. Then he ends up revealing that he is talking to a psychoanalyst, meaning he is getting the help he had been searching for before.
Therefore Holden is a dynamic character.