Why did Barzini try to kill Michael in Sicily? The killing wouldn't go unavenged
Perhaps he tried to have Michael killed to prevent Michael from eventually avenging Sonny's murder. Then you might ask, why did Barzini agree not to interfere with Michael's return to the US? Because he and the other Dons were greedy for the drugs profits Vito's political protection would open up. They deluded themselves into believing that Michael--who had already shown his stuff by killing Sol and Mac--wouldn't be a threat to them. Greed trumps caution every time
Barzini probably thought, they could take Michael out, down the track, in the Corleones 'weakened' state, once the drug operation was up and running
