Because Aatrox can use Triforce's passive really well. Taking towers are easier with sheen proc and attack speed. You will deal alotta damage and heal alotta hp with sheen procs + passive + E + auto attack. You don't rely only on Q hits, you can auto attack and you'll still deal good damage. Whereas with Black Cleaver you only rely on your Q hits for damage and auto attacking doesn't deal relevant damage.

Death's dance improve your passive Physical Damage healing along with Ravenous Hunter (Ability Damage Healing) rune. Visage will even further imrove all healing. You don't only deal alotta damage you also heal alotta HP in fights.