Arthas’ reasoning was arguably twofold. From a practical standpoint he thought an Azeroth united as Scourge could better stand against the Burning Legion, but behind even that reasoning was the less practical and more emotion-driven need to justify what he’d done by “saving” Azeroth.
Scourging the entire world might feasibly stop the Burning Legion from ever invading again, but moreover it would retroactively make every heinous wrong he’d committed toward that end “right.” Basically ever since Stratholme - whether one agrees with his reasoning in that specific instance or not - Arthas remained on a course of accruing more and more sins in the belief that when all was said and done, the payoff would justify him and the world would be able to look back at his misdeeds and judge them all necessary and worthwhile sacrifices.