Thats a lie. His kit could have easily been balanced. Its a lie that Riot peddled to justify deleting a champion right out of the game.
All you had to do was decrease his healing, increase his toughness or provide small way to mitigate incoming damage, (such as during his ult, or part of his passive) let his damage and healing both scale off of AD, not off of max HP, and turn his ult into a form of team fight buff. Keep his E magic damage, and let it do some kind of torment, where enemies receive extra damage when hit by Aatrox or allies, or provides vision on them for x seconds.
There were countless ways his kit could have been balanced. To say it wasnt possible is fucking absurd, and shows your limited thinking, or your propensity to swallow whatever bogus load of crap Riot puts out.