The rhyme is pi/hŭi/kwi; tones match. The cuckoo is a symbol of the Emperor of Shu who longed to go home but was unable to make his dream a reality. After his death he metamorphosed into a cuckoo. The song of the cuckoo expresses the pain of not being able to go home—puryogwi—in the sense that going home is always best.
The sun is going down; I stand alone outside the double brushwood gate.
Three times the master has shooed me away with his hand.
The cuckoo knows our heartless culture;
it sings in the woods that it’s better to go home.