I am fond of music I think because it is so amoral. Everything else is moral and I am after something that isn't. I have always found moralizing intolerable.
A little OT, but soul may excite the lower material proclivities as well. It's a matter of patterns.
So the title of this post should more rigorously sound like 'Why does some kind of music excite the soul?
The answers given above are pretty generic, no offence at all meant for SI and EricB. My answer is still worse since I have no answer, lol.
But I can tell you that the pattern is relevant here. We should fall back on the science of psychoacoustics and underline which are the harmonies and melodies and patterns typical of spiritual music and which are the ones typical of other musics.
This way we'd have an objective answer.
Then there is the subjective answer, one piece of music I like may cause headache to others (it definitely is so!)
So spiritual music objectively inspires spiritual thoughts, whereas, according to our own mental patterns, even other kinds of music may excite the soul.
I am excited by the melodic minor changes and melodies played in jazz music and improvisation, for example, with many dissonant notes and tritones.
Whereas tritones were called 'the devil in music' just a few centuries ago.