A catchy song is one that you like. There's SOMETHING about it (maybe the singer's voice, or the chorus, or the music in it) that is really good and gets your attention. It may not be a very good song, but you still listen to it.
Thanks a lot, Barque. I've never doubted your native-like English. But this time let's wait for a native speaker, if there is one reading this thread, to confirm for me. I beg to do so is just because there are many "catchy songs" in China nowadays, you might have heard one or two of them. In Chinese they have another name, brainwashing songs, but some actually are positive.
I tend to believe "a catchy song" is neutral and negative. Sorry to disagree with you.