Perhaps you were aiming at this.
And in a way, you succeeded. Certainly, you called into question the military machine. Still in a landing pattern after the second war to end all wars, the machine was gearing up for Korea, then Vietnam, without so much as a touch-down or reverse thrust. It was, is, as illogical as your Catch-22. We were desperate for an anti-war novel and absurd was the correct form, with your story and sentences wandering around and around popping out from insane fox holes. In a way it is an appropriate bit of banter.
And you did discuss some important issues: justice, fate, mediocrity, the frailty of humanity, non-conformity, perseverance, but the pacing is pretty unendurable. My reaction was that you would have to be under orders to read the whole of this.
Our cultures do need the words against war so desperately, and your book doesn't fall apart, it maintains its form, excruciatingly, to the end. So that is something. But the book ends where it begins. It talks against war, but in the end, there is no alternative offered. You have gone AWOL. One by one the troop is taken, shot down, mutilated, and we are left yawning. You have not even made us care.
And in the meanwhile you have uglified life, uglified women in particular, ascribing no dignity, even off-handedly, to any female character in the book. You may, like Henry Higgins of My Fair Lady, defend yourself and say that you gave no dignity to any character in the book, but that is not true. Your ending does grant dignity to Orr, Yossarian, and the chaplain, but ends with one last denouncement of a female character as, at best, maniacally dangerous.
Catch-22 is unkempt, unfair, and ridiculous. Absurdity is not inappropriate, but it does not stand on its own. You have given us a few helpful vignettes with Clevinger revealing an underbelly of injustice, Wintergreen posing as the erratic hand of fate, Major Major exemplifying the horrifying result of exulted mediocrity, and Milo Minderbinder giving us a frightening look at unbridled capitalism. However, I am mystified that it is rated highly on either of the Modern Library lists.