tower of babel was the pivotal moment when the league decided to kick batman out. why? beucase 1st of all ra's al ghul was making another bid for world domination, but first he had to neutralize the league.....too bad he did it with the stolen countermeasures that batman had for the league just in case they went rogue(Talia broke into the cave and stole his files)
supes-red kryptonite(not lethal but extremley painful)
Kyle-ring was put on his finger during sleep and hypnotized into thinking he was blind...willpower, and imagination being the cause of that
J'onn-fire of course
the rest i dont remember
in addition to all that, Ra's had created some sort of global scambling device that rendered the world in pure chaos by disruptiing either sonic, or brain wave patterns(cant remember which). anyway the resulting effect was all the languages in the world was scrambled,(like the biblical tower of babel)while ppl heard the sound of THEMSELVES just fine as if nothing was wrong , the sound of everybody elses speech to thier ears was all babble to them. and chaos ensued and it worked for a while too, and he would have gotten away with if it werent for those darn leaguers who work together so often they could communicate in the language of combat, and had no need for speech...... that and the fact that j'onn eventually established a mind link.