Kate and Ethan are very different people, but they bond over their mutual love of the arts - in particular, books and music bring them together. The second time they meet, Kate is reading The Catcher in the Rye by J. D. Salinger. They have a conversation about the work, and Ethan says, "The whole thing seems somewhat bitter to me now," to which Kate responds, simply, "That's why I like it."
I chose this book with a specific purpose in mind. My idea is that Kate, who has a hard time conveying her true emotions, appreciates Holden for his ability to express his feelings at face value. And sure, Holden Caulfield may be somewhat mental, but he's also painfully real. Modern-day audiences are getting a similar story in The Perks of Being a Wallflower, which is also about a social outcast. But that novel is more upbeat than Catcher. Like Holden, Charlie is introverted and intelligent beyond his years, but he's also more hopeful and able to engage with other people. Holden isn't really headed for anything positive, and he has a general apathy for others and inability to connect, but he approaches the world with a sort of grim reality that is somehow refreshing in its honesty.
I think that's what draws Kate to the story, and it's partly what draws her to Ethan - his no-holds-barred approach to life. But Ethan, though troubled and angry, has hope, which is his most redeeming quality. He's able to see the potential in others, and particularly in Kate, which is why he's no longer interested in a character like Holden.