an interesting sideline - John Lewis, who early on was touting Ornette as the first thing new since Bird, was saying in his last years that Ornette, in the years since, had lost it and was faking it, basically - disappointing in someone who is held out as Ornette's early supporter. But than, I think Lewis was very pretentious and artificial in his approach to the blues. Apparently, once he sensed that Ornette was no longer "in the tradition" he felt artistically betrayed.
"Anti jazz" would indicate that the new music was counter to whatever the critic felt was essential to jazz - and that would be recognizeable melody (and Ornette played, at least in those early days, with an implied sense of harmonic development as well as melodic) and the whole idea of getting from A to B to C in an "organized" fashion. And those DOlphy/Trane things are frighteningly intense, not for the faint of heart. And certainly Tynan wasn't the only one. Ira Gitler is still railing about the sound of the first generation avant garde, and as I recall Leonard Feather was quite nasty as well. And I am certain there were more than a few other critics who agreed silently, but were too diplomatic (and too sympathetic to the problems of the jazz musician) to take a public stand that would have put these guys, whom they knew were great musicians, down. People like Gitler took it personally, interestingly enough.
Ornette's bands in the 60's, also, were well organized in a relatively conventional jazz way, the elements clearly delineated, less chaotically tied together than in Trane's band. I heard Ornette with Haden and Dewey Redman (and I think Billy Higgins) at Slugs in 1969 and it was an overwhelming experience. I didn't really understand it but I knew it was ingenious and I felt something very deep stirring in me afterwards (and thankfully Haden came over between sets to talk to me and my friends and try to explain what was going on. )