The composer writes (the original text was in Japanese): "The Doraemon character Nobita has special skills -- Nerukoto and Ayatori. I think they both are excellent skills. Now then, here's a question: What do you call Ayatori in English? The answer: Cat's Cradle!" He goes on, but I haven't looked closely enough to translate the rest.
I don't know what "Nerukoto" is (and I've not seen the cutesy kid's show Doraemon other than trailers), but it's written with the kanji for "go to sleep". So, I think he discovered the English term for Ayatori and found it ironic that it involves not only the concept of sleep with the word "Cradle", but of course Doraemon is a "cat-type robot" ...
OK, here's the original text, including the bits I haven't translated yet, for those who care to beat me to it: