How does Holden's red hunting cap or the Museum of Natural History show Holden's coming of age in The Catcher in the Rye?

Throughout The Catcher in the Rye, it's clear Holden is fighting his growing up, which is symbolized perfectly by his enjoyment of the Museum on Natural History. In Chapter 16, Holden says he enjoys the museum because "everything always stayed right where it was."

This part of the novel encapsulates Holden's fear of coming of age completely. In order for me to fully explain Holden's feelings about the Natural History Museum, some background is...

Throughout The Catcher in the Rye, it's clear Holden is fighting his growing up, which is symbolized perfectly by his enjoyment of the Museum on Natural History. In Chapter 16, Holden says he enjoys the museum because "everything always stayed right where it was."

This part of the novel encapsulates Holden's fear of coming of age completely. In order for me to fully explain Holden's feelings about the Natural History Museum, some background is important. A few chapters after he discusses the museum he sneaks into his home to see Phoebe and explains why he sees himself as a "catcher in the rye": 

"I keep picturing all these little kids playing some game in this big field of rye and all. ... 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 over the cliff..."

It's this feeling about rescuing kids from adulthood and the accompanying "phoniness" that pushes Holden throughout the novel. So when he thinks of the museum, he thinks of his own childhood. He wishes he could secure it in airtight rooms and he, and all other children, would not have to proceed to adulthood. When thinking about the museum but really referring to the transition from childhood to adulthood, Holden says, "Certain things they should stay the way they are. You ought to be able to stick them in one of those big glass cases and just leave them alone."

In addition, this is why the word "f--k," when inscribed in the museum, shocks Holden so much. He's attempting to protect kids from adulthood and, in this sanctuary of youth for him, he sees the worst of the adult words.