Nobody knows, but similar poems have been going around the school yards since at least the mid-1900s. The tradition of self-contradictory poems in general goes back even further, at least to the Middle Ages. The oldest known one is from a circa 1305 poem called 'The Land of Cockaigne', but since it's written in Middle English, which I only understand a little of, I can't locate the exact stanza.
The Land of Cokaygne - Wikisource, the free online library
Incidentally, this might be the origin of the word 'Cockney', although some people think it comes from 'Cocken Ey', meaning 'A Cock's Egg', i.e. something that doesn't make sense.
