i think its kinda how uchiha shisui said. maybe he considers himself the most powerful, but thats boring if you cant fight powerful guys. so he allows sasuke to live in hopes he becomes strong enough to challenge itachi. i dont thin k itachi left him alive to be an avenger, i think he left him alive to have someone worthy of fighting int he future. the rest of the clan was incapable of ascending to a higher level so they were dead to him. sasuke might reach a higher level so itachi left him a live.

i think itachi initially saw himself becoming evil and arrogant and warned sasuke, and now that he has he doesnt really care anymore.

i used to think he did it for some weird altruistic reason, maybe he did save sasuke from brotherly love or whatnot or maybe for some strange reason involving the akatsuki but i dont think so anymore. i think he really is an evil powerful guy who wants to test his strength and skill against only those that are worthy.