I stepped on the cat

Yuika is learning the piano and this is one of the first songs that she mastered. My husband tells me the song means "I stepped on the cat's tail" but I think he's a liar because the word "tail" isn't in the title, so I'm thinking it just means "I stepped on the cat".

Here's the piano version:

Except that she knows the song so well that she will play it in high speed. And when she's frustrated at learning a new song. And when she's bored. And when she's not bored. Basically at all times when she is in this house that is not eating or sleeping, this song can be heard.