sure, any song can be broken down to "ok, this song is in the key of C#m, it is in 4/4 time, it uses a so-and-so diminished chord here, and a so-and-so augmented chord here" but do you really think that that is what was going through the songwriter's mind when he was writing the song? he was probably trying to express out a thought or emotion, or perhaps just a general wondering. now sure, he may have used theory to write it (especially in classical music) but that doesn't mean that only people trained in music theory can appreciate the song"..
Ok, , when you're writing music you just dont put any chords on it like snap there it is a sad song. you have to think about how its going to sound when you play it, will it sound sad, or happy or angry or sexy?,depends on what you want to do. then after putting the chords you think about the solo, you go back to the chords to "analyze" what chords you're using to make the melodies for the solo. /so what you' re really doing is you're analizing a problem because you're trying to find a solution on how to make it sound the way you want it and yeah it is like a math problem. just playing and counting how many quarter notes or eight notes or even counting on what beat you're gonna do a pause or rest is math. And that's whats really going on inside the mind of a songwriter, Unless you have a really sad lyrics telling the listeners that that song is very sad, you cannot just put any chords on it to make it sound sad.. what if you're writing an instrumental and you want it sad and because its instrumental theres nothing to tell the listeners that its sad except for the music itself, so you dont just put A major and D major and G major on it cos it wouldnt sound sad because those are happy chords, you have to use something like Bm and F#m and A and E major to make it sound sad. you want it scary? use something like Em then Dm then Cm then B minor then C to make it sound scary or spooky. Every chord progression in the book expresses an emotion.