Because idiot is the word everyone uses for Myshkin, the word he uses for his own past, and the word that closes the book: the title is the name of a problem, not just an insult.
In Russian, idiot has two uses in the book that intersect. It is a diagnosis: Doctor Schneider treats idiocy and madness at a sanatorium in the Valais, and the prince says his fits had made him "almost a complete idiot." And it is an insult: Ganya calls him a damned idiot, Aglaya murmurs the word at the Vauxhall, Nastasya asks, on seeing him at the door, "what kind of idiot is this?", and the prince himself, after offering money to Burdovsky in public, says "Yes, I am an idiot, a real idiot!"
The last page returns to the word: the narrator imagines Schneider, seeing the prince beside Nastasya's body, making a gesture of despair and saying, "as he did back then," Idiot! The circle closes, because the prince is back in the state he set out from in the first chapter.
So who is the book's idiot? For some, it is the prince, sick and naive; for others, those who judge him that way and do not see what he sees. The text sustains both readings, and the choice of title is what keeps them open.