It's pretty similar to music, yeah. Or perhaps music can be similar to poetry. Just this morning I was re-reading the lyrics for "Pale Green Things" & "Woke Up New" by The Mountain Goats. There's a sort of specificity in intention that the form tends to end up dictating, that can really carry a rich emotional context or metaphor more directly into the listener's brain.

(Of course, prose is sort of like a superset of poetry - it's not a hard dividing line. You may find especially poetic lines in your favorite longform works, especially in good fiction books.)

I do think that many English teachers do a poor job of encouraging a love, or even understanding, of poetry. One of my highschool teachers was in love almost with categorizing the forms of poetry - sonnets and sestets and villanelles, and seemed to think that if we learned the rules about what lines had to rhyme or which syllables to stress, we'd enjoy poetry. I hated it! But then the next year, even against this backdrop of learned avoidance, my teacher was so in love with the ability of poetry to communicate - the unfolding of a few words into meaning like a flower in bloom - something clicked. He focused almost not at all on the structure of poetry, but rather on finding works that spoke to you. I'm still not a lover of poetry, even now, but I have poems I appreciate.