In the movie "Lord of the Rings: the Return of the King", why does Frodo have to leave on the ship?

Its not that Frodo "has" to leave but more a willing choice that he makes at the end of the movie. He was injured in the first movie, and has been living in constant pain. The elves would be able to help the process and they welcome him with open arms. He also portrays a character that is just very tired. He just doesn't have the same goals and thoughts of the rest of the hobbits. Frodo leaves for his heath, peace of mind, and to get away from the lonely, unsuited life in the Shire.