There’s no reason why you can’t analyze music the same way you’d analyze a poem.
At least, when it comes to lyrics. If you don’t really know anything about the structure of a song, musically speaking, you’re probably going to have some difficulty speaking to that—although there are some things we might notice intrinsically, like the shift from a major to a minor chord or the pace and rhythm of any given song, so I guess even then you can call those into question when you’re looking at a piece critically. But when it comes to lyrics? It’s pretty much the same thing as dealing with a poem, if you understand that the reason repetition happens might have more to do with the musicality than the reason (though, then, why these words? Should it contribute to the overall meaning of a song or is it there because it sounds right and fits within the beats?).
Looking at music is probably a better way to introduce people to the act of close-reading, if that’s something you plan on doing ever. It’s easier to grab a song everybody likes, that they already know the words to, and then pick it over. For one thing, they might already have a general understanding of what the song’s about, and for another, they might be more willing to dig in deep with it. Songs don’t have to be hard to read.
I’ve done a lot of work with “Rime of the Ancient Mariner,” and it’s a pain in the neck to get through, but it’s also contributed to some frequently used phrases in English literature that either can be very easily attributed as allusions to it in other works or not—since they’ve entered the common vernacular, it might just be like some kid saying “It’s all Greek to me” and not knowing that it came from Shakespeare. I also like the band Bastille.
Look at the song “The Weight of Living, Pt. 1.” When someone’s got an albatross around their neck, they’ve got a lot of guilt weighing them down—and that comes from “Rime of the Ancient Mariner,” when the titular character is forced to wear the carcass of the albatross that he shot down from the sky. The song itself makes it pretty clear what that albatross is doing, since to be honest there isn’t a whole lot of depth in the lyrics of this one—there’s a lot of repetition, and not a whole lot of saying anything new, and besides, the title tells you what the main concern of the speaker is—but being able to say something like, well, this albatross is an allusion to a much longer literary work that deals with guilt and the need to expel it by talking about the thing you feel guilty over, you might be able to get a little bit more out of the song. It encourages you to let go of the thing that’s holding you down, sure, but how are you going to do that? If you follow the allusion and grab Coleridge’s Mariner’s solution, you’ve got to admit that you’ve made a mistake—but once you do, you’ll be free of the guilt (for at least a short while).
There are much more difficult songs to look at though, and definitely some that more people like. I guess it would be fine to figure out where whoever you’re showing how to do a close-reading is when it comes to their ability to analyze words. Figure out what kind of music they already listen to. Find a song that matches a work of literature, and then do the two together. I prefer doing close-readings of poetry because I feel like it’s typically more compact, a little easier to sift through and figure out what’s going on, even when the poet is being deliberately obtuse (looking at you, T.S.Eliot).
That said, people do close-readings of songs all the time (songmeanings.com is a thing), even if they don’t really call it so. Music with lyrics is probably the closest and easiest way for people to interact with literature lately, because all they have to do is turn on the radio while driving. It’s important to remember that English language skills are as much verbal as they are written, and for a lot of people, verbal skills are going to be ultimately more important. Being able to figure out what people are saying while they’re saying is an important ability. If you can catch a joke .5 seconds before anyone else does, you feel a little better about yourself, I think.
But besides the practical reasons why you’d want to be able to analyze a poem or a song, there’s also the fact that for some people, analyzing things is fun. It’s an enjoyable exercise. While you’re probably not going to run out of poems to analyze any time soon, if you can impress your friends at a party by explaining the nuances of an NWA song, why wouldn’t you?