Part of the problem, I suspect, is that most people have very particular taste in poetry. (So particular that some people might never discover their own!) It doesn't help that there is a lot of bad poetry out there, as well as poetry that might be good in some superficial "academic" sense, like you described, but doesn't produce any reaction in the reader.
There's also the fact that reading poetry is so different from reading regular prose, and it can take some getting used to. It took me several re-readings before poems that I now love first started to "click."
For me, it all started with discovering Nabokov's novels last summer -- his writing sparked an appreciation of prose and imagery that I never experienced before, despite being a lifetime reader. I read that he loved Keats, so I picked a few of Keats's best-known poems and read them over and over, until I internalized them and eventually came to love them. As I've explored other poets, I find that the more I read, the more I become sensitive to. But still, I'd say that 80% of the poetry I encounter (especially modern stuff) leaves me feeling stupid and insensitive, at least after the first couple readings. Better than the 99% a year ago, though!
EDIT: I went through something similar with classical music a couple years ago. Despite being a musician and music lover, I could just never get into it. I immersed myself in it for a few months and began to see/feel the beauty in it. I think it's just a very different way of approaching music compared to modern genres and structures, kind of like how poetry is fundamentally different from the novels most of us grow up reading.