I am not sure that classical has been a spent force for the past century. Sometimes ossified, sure. But it's a lot like Broadway - often declared dead but still hanging on. I agree that most atonal music is unlistenable but some of the recent post-serialism composers may well stand the test of time. I just got and have been blown away by William Bolcom's Songs of Innocence and Experience, for instance. Ned Rorem, David Diamond, and others are some who will stand the test of time. And though they were close to or completely atonal (or at least weird in a good way!) at times, I like Alban Berg, Charles Ives, Edgar Varese among other early 20th c. avant-gardists. (Frank Zappa was a big Varese fan, BTW)
As for the original question of why some people prefer jazz or classical the best stab I can take is that music, more than other art forms, hits you more in the gut than the head. Musical preference is a matter of one's individual emotional makeup and experiences...hence ultimately unknowable and at best imperfectly explainable.