Holden may use words like “bastard” and “ass,” but he has to draw the line somewhere—and he draws that line at writing "fuck you" on the walls of elementary schools and museum tombs. These places particularly bother him, because they remind him of his own relatively comfortable and happy childhood. In Holden's world, everything has been corrupted by vulgarities. Even his own death, he says, couldn't be sacred or peaceful, since someone would probably write a "fuck you" on his very tombstone.
We argue in Holden's "Character Analysis" that it's no wonder that he sees sex as dirty and degrading, when all the portrayals he's seen of sex are in fact dirty and degrading. This is one such portrayal; Holden imagines a "perverty bum" sneaking into Phoebe's school at night to write the message on the wall (25.16).
Hate to break it to you, Holden, but it's way more likely that a student at the school vandalized the wall. But Holden can’t see that. In his world, children are innocent and adults corrupt. While this keeps everything nice and simple in Holden's mind, it also makes it impossible for him to really understand the process of growing-up. While he does realize that trying to rub out all the "fuck you"s in the world would be impossible (“you couldn’t rub out even half the ‘Fuck You’ signs in the world” [25.18]), he doesn't make the important connection that it would be futile anyway. Kids grow up—and sometimes they even write “fuck you” when they’re still in elementary school.