Answer: "a cuckoo"
Two or three weeks ago I posted HERE about 두견 (杜鵑), a word used to refer to both "an azalea" and "a cuckoo." Another name for the cuckoo bird is 불여귀 (不如歸), which literally means "not (不) like (如) returning (歸)," but which should be translated as "not as good as returning." Now you might be thinking, "What?" Well, it seems the Chinese pronunciation of 불여귀 sounds similar to the cry of a cuckoo bird, which is how the bird supposedly got its name.
According to one story in Chinese mythology, there was an ancient Chinese kingdom known as Shu (蜀 - 촉) with a ruler named "Emperor Wang" (望帝 - 망제). One day Emperor Wang was walking along a river and saw what looked like a dead body floating in the water, but when he approached the body, the person he believed to be dead suddenly and surprisingly opened his eyes. The man said he was from a district called Xing-zhōu (刑州- 형주) and that he had come out to the river and accidently fallen into the water, after which he floated all the way down the river to where he was found. He said his name was B 鱉靈 (벌령), which means "Turtle Spirit."
Emperor Ming felt that B must be a good man since Heaven had spared his life, so the emperor gave the man a house and made him one of his counselors. Later, however, Bie-ling deposed the emperor and banished him to another country. The emperor was so heartbroken and homesick that he eventually cried himself to death, after which he transformed into, you guessed it, a cuckoo. After Emperor Wang's death, people said they saw a cuckoo, which they believed to be the spirit of the emperor, flying around crying in such a way that it sounded like he was crying the Chinese for "It's not as good as returning," which can also be translated as "It's better to return."
There is, at least, one other story of how Emperor Wang became a cuckoo, but the story I just paraphrased came from THIS Korean Web page. You can imagine that poets and songwriters might come up with a few ways to use the double meaning of 불여귀 (不如歸) in the material they write.
By the way, 불여의 (不如意) is a Sino-Korean word that literally means "not (不) as (如) intended (意)." My dictionary defines it as "to go wrong [amiss]" or "to go contrary to one's wishes."