Sasuke says it again and again. "He left be alive to be an avenger. That is what I am I must avenge them." Then he usually does a chidori and runs recklessly at whatever is in front of him. Point being the manga implies that from sasuke speaches and itachi's diologue. Itachi left sasuke alive to he could get the super sharingan and maybe kill him one day if he truly deserved to be killed because of his actions.