1)Thats the way the choosen! anyway if he killed only Barzini, Tattaglia would get into drugs get the support of the other families and drive the Corleone family to the hell.
2) Barzini and Tattaglia killed, then the other families would say the Corleones are triying to get control of the buissness and move them out.

That means: He was forced to do it, maybe it felt good too, and if I were Michael I would do the same... In that buissness you can take no chances!