The peace agreement was just a ploy on both Corleone and Barzini to buy time in order to plot the others inevitable demise. Barzini could not survive for Corleone's peace of mind and continued strength, and in order for Barzini to become the most powerful Don, Corleone had to be eliminated.
"Joe Bananas went after Carlo Gambino, the war went on for seven years..... When guys go to the mattresses, they're not out earning" -Tony Soprano
