But as I say, I agree with you on most other Jazz though. And I'm convinced that about 80% of the people that go around saying they love jazz are just pretending to.
Also, along with Bluegrass, jazz is SO closed off to people who'd like to join in and play with a group. It's filled with gatekeepers and judgemental jerks. For instance, criticizing you for bringing a guita they don't agree with, "you can't play jazz with that, go home and get another something else there, Eddie Van Halen". Seriously, it can be that bad.
That's not been my experience playing jazz around my local area. I've never played jazz in New York but I have heard that all manner of ungentlemanly behaviour goes on in jams there and I suspect I'd be on the receiving end of it if I dared to try. Presumably acceptance of the newcomer is determined by the size of the existing pool of talent. Rural England is not well supplied with jazz musicians of any skill level (or discerning audiences) so we can't really afford to treat them rudely. I'm not really a guitarist, but the last time I played one at a jam it was one of these: https://www.andertons.co.uk/brands/gl-guitars/asat-guitars/g...
But what is your definition of "jam" then? Is it improvised at all?
I have the opposite approach; I like classical music very much and have listened to it a lot, but for many years now I've only been improvising; the idea is to sound in real time as if it were composed and practiced; meanwhile I can play a whole band live myself (e.g. http://rochus-keller.ch/?p=1268). I've always found it a torture to read and learn a piece and always play it back the same (correct) way.
Musically it's a combination of atmosphere and passion with a cerebral edge, with harmonies that are spicy and colourful but not atonally exotic and incomprehensible.
It's improvised moment-by-moment riffs and conversations over a chord chart and some loose linear and structural traditions. It doesn't have the grand architecture of classical music or the cheeky crowd-pleasing crudity and playfulness of pop.
Genres either hit you or they don't. It's fine not to like something.
Here's the tune Softly, As In A Morning Sunrise, as Sigmund Romberg wrote it:
https://www.youtube.com/watch?v=Uy_L8VVu7-c
And now, as a variety of jazz musicians heard it:
https://www.youtube.com/watch?v=XSeFc3CP5Mk
https://www.youtube.com/watch?v=VlViBYcZpJ0
https://www.youtube.com/watch?v=2NG_wZFBM24
https://www.youtube.com/watch?v=dofsqZrE5sU
https://www.youtube.com/watch?v=WaV51BuHfIw
Do you hear how the melodic theme is stated, before the players improvise over the same chord progression? Do you hear how fragments of the main melody are woven into the solos? Do you hear the interplay between the musicians as they rotate between accompaniment and soloing? Do you hear how each ensemble creates a distinct mood from the same basic starting point? If you do, then you're starting to hear the language of jazz.
Listen to the Brubeck Quartet's "Dave Digs Disney".
If you still "don't get" jazz after that experience, my guess would be that your formal training installed dogmatic opinions.
IMHO, that's so unusual in a jazz setting that it's almost always expressly declared as such - ie "free jazz" or "experimental". And even that relies primarily on preparation and practice to be done well.
IMHO, performing jazz is a delicate process of painting within the lines - so that you don't tread on the toes of everyone playing with you - lines you are all expected to know if you are going to get on stage and play a specific song together - while creating the illusion that you are all just messing about. And you are doing that while navigating a complex conjugation of harmonic structures, substitutions and alternatives, while seamlessly recombining the songs' melody with jazz idioms, rehearsed licks and runs, and admittedly, some improvisation, all while you try to say something new and original that your audience will be interested to hear.
So, you have to lean a lot on preparation and personal rehearsal (and group rehearsal), because you are listening, reacting and managing so many things at once that if you can't rely on muscle memory to keep up with the chord changes, and haven't sufficiently navigated several ways through them ahead of time (what if one of your bandmates decides to reharmonize some section in a way that precludes the scales you were planning to use to get through it?), you'll fall on your face.
Take a close look at Bach’s violin sonatas; they seem like jazz to me compared to a lot of his work; they have lots of wild chords with 7ths and 6ths and 2nds, they are wandering and improvisational feeling.
Some jazz gives me the same feeling you’re describing, and I think you’re onto something with it being fun to play… a lot of it is musician’s music. Watching sporting events gives me the same feeling… good for the players, not as good for me, I’d rather be playing, or doing something else.
There's so much going on in 'jazz' music, but for me personally I'm always listening to it (and all music, really) rhythmically first, and all the harmonic and melodic components, everything else, comes out of the rhythm. That tends to be the opposite approach of European classical music (which of course I like too).
I don't know what your taste in music is, but there's a ton of great music out there that falls under the label jazz. Since you're in the classical world, here's some recordings that might speak to you:
https://www.youtube.com/watch?v=0VlOigfm-ww
https://www.youtube.com/watch?v=YMTHsK3MlzA
https://www.youtube.com/watch?v=OIIyCOAByDU
https://www.youtube.com/watch?v=w0O9L7KXkC0&list=OLAK5uy_l61...
And some live: https://www.youtube.com/watch?v=Y_BE_gi4YkA (my friend's group)
https://youtu.be/lhgaJ_kDLPg?feature=shared&t=23 (particularly Afro Blue)
https://www.youtube.com/watch?v=GuEVN3BTFHM
https://www.youtube.com/watch?v=-DGY9HvChXk
https://www.youtube.com/watch?v=oA9GhIyP_zI
https://www.youtube.com/watch?v=lM5Cj8yFkOQ
I don't know, the rabbit hole is deep I could go on forever.
This video is an excellent musing on creativity and learning that I think is relevant even for nonmusicians.
suggestions: Tony Williams Lifetime, Miles Davis 1969 - 1975, Mahavishnu Orchestra, Jaco, Weather Report
Davis's music is pretty much about as pure rhythm as you can get outside of electronic music. it's so far beyond jazz that you can hear so many modern genres in something like On The Corner, it's crazy. and it was hated originally, too. jazz rejected evolution, so now it's stuck as some dead academic genre
Also, "classically trained" is irrelevant. Having a background on a specific kind of music doesn't grant you authority or insight into a different kind of music
I just don’t get jazz at all. It’s fun to mess around on stage, and play free form. But it also ends up sounding that way to the listener: like some mess that must be fun to play…
I was stuck on a long drive a couple of years back, driver had Swissjazz FM on the whole time. Felt like a form of torture ;)