I think what may be most appealing, among the many characteristics of Jazz, is that, in most of its forms, it draws the listener deeply into the music-making. It swings, and that is certainly a powerful lure, but our involvement doesn't stop at finger snapping or toe tapping. Jazz, most of it anyway, is grounded on compelling melody lines and the artistic improvisation built around them. Great jazz groups are united in a particular performance and they welcome the listener to join in. Whether "in our heads", or by whistling or humming along, we can't resist adding our own improvisations. Or maybe we just mentally maintain the melody line or chord structure, and by doing so get a clearer view of the improvisation we're hearing. Unless we are sophisticated musicians, we may not "understand" all of it, but we are personally and rather intimately involved and we love the trip. Over time, great musicians make clear to us the multitude of different and wonderful trips that can be taken from the same "roadmap".
Having said that, I recognize that I've fallen short of what I'm trying to articulate, but I think if you love jazz, you'll have an idea what I mean.
Now, back to my qualifier, "...in most of its forms.." , and the question which follows from it. I think that Free Jazz lacks the hook I've tried to describe, and for me that makes it unappealing despite its other attributes - great musicianship, etc. I keep trying, but I just can't get into it. What is it that Free Jazz offers to its fans? How can one go on the trip without the roadmap? What is it that I'm not hearing?
Perhaps this is just another futile attempt to put one's reaction to art into words, and the only answer I should expect is, "If you have to ask, you can't afford one.". If so, so be it.