I mean, I listen to songs just to enjoy them but other times my head breaks in to a stream of consciousness 'why does this song work' deal. I think because at one point I had to relate to people about what made a CD great and communicate such things, my head and ear just adjusted to breaking it down a bit.
It's a marriage of things that make a great song but the only key is that it communicates something to feel. that's something you can't learn in as much as develop how to communicate a feeling.
Then you can get in to things like song structure, song tension, lyrical content and the like.