Are there any instances of sexism expressed as a theme in The Catcher in the Rye?
Holden is a very sweet and caring guy, but he is also a teenager and a product of his times. The book, published in 1951, but begun in the 1940s, predates the era of the modern women's movement, and Holden's views of women tend to be traditional. He objectifies Sally Hayes in her skating outfit and calls her stupid. He tends to think of women primarily as sex objects: after all, he is a teenage male and he wants to lose his virginity. While is not unkind, he does stereotype females:
The trouble with me is, I stop. Most guys don’t. I can’t help it. You never know whether they really want you to stop, or whether they’re just scared as hell, or whether they’re just telling you to stop so that if you do go through with it, the blame’ll be on you, not them. Anyway, I keep stopping. The trouble is, I get to feeling sorry for them. I mean most girls are so dumb and all. After you neck them for a while, you can really watch them losing their brains. You take a girl when she really gets passionate, she just hasn’t any brains.
So he presents a puzzle: when a woman says stop, he stops. On the other hand, he says "most girls are so dumb and all."
Yet for all his interest in "girls" as sex objects, Holden gets upset at the idea that Stradlater will have casual sex with Jane. Holden holds to traditional notions that sex should occur between people who care about each other and share mutual respect. He clearly sees women as people with feelings that are important in a relationship.
Thematically, sexism would fit under the category of phoniness: Holden dislikes the falseness with which guys like Stradlater seduce girls, and he strives to see people not in terms of categories but authentically. To the extent that he is able to really see and respect others, he functions as a non-sexist character. On the other hand, he does reflect the values of a sexist time period and is a flawed person who ironically can judge others superficially while simultaneously wanting to transcend phoniness.
Holden is unable to relate to females, and in his false bravado he sees women as sex objects only. Holden meets several females in the book, but most of his encounters with them are surface encounters, like meeting the girls at the Lavender Room. He is critical of the girls, who are acting superficial, looking for celebrities. Holden also meets Sunny, the prostitute, who argues with him over the amount of money he owes her, even though they don't do anything together. These encounters just help to secure Holden's belief that women are "phony" and no good. Even when he pours his heart out to Sally Hayes, he receives no sympathy, and this just makes him more angry at women. Holden is an adolescent who is struggling with his budding sexuality and struggles to understand women, and in this struggle he comes across as being very sexist at times.