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I went down by a different staircase, and I saw another "Fuck you" on the wall. I tried to rub it off with my hand again, but this one was scratched on, with a knife or something. It wouldn't come off. It's hopeless, anyway. If you had a million years to do it in, you couldn't rub out even half the "Fuck you" signs in the world. It's impossible. (25.18)
Then again, he is also impeded by the inherent impossibility of his task. There's just too much filth in the world to ever get rid of it.
That's the whole trouble. You can't ever find a place that's nice and peaceful, because there isn't any. You may think there is, but once you get there, when you're not looking, somebody'll sneak up and write "Fuck you" right under your nose. I think, even, if I ever die, and they stick me in a cemetery, and I have a tombstone and all, it'll say "Holden Caulfield" on it, and then what year I was born and what year I died, and then right under that it'll say "Fuck you." I'm positive, in fact. (25.39)
Check out how this passage connects two of Holden's major obsessions: mortality and the "filth" of the world (which many would categorize under "loss of innocence"). This reminds us that, in a way, growing up, getting exposed to "filth" and various "fuck you"s, is a sort of death in itself.