Hi Meddler! I love when you pop in like this! It's so great! :3
These are my thoughts on Aatrox's identity/theme:
I always thought of him [Aatrox] as an artisan of war and death. You can definitely see it in the way he handles his sword and especially his quotes, like: "This battle will be my masterpiece" or "Rage against the dying of the light" or "Violence is elegance." To me he comes across as a graceful and yet sadistic warrior.
He's not the kind of entity that would think: "I will empower my allies." Quite the contrary actually; Aatrox just wants people to fight, to bloody and bruise each other, and to lose themselves in hate and rage ("Some fight for honor, some fight for glory. It matters only that you fight."). That's why he could never be a Tank or someone that sets up for his allies. Honestly, from a thematic standpoint I can't imagine that he considers anyone to be his ally or friend (heck, just look at his Champion Info page... he's only get one recognized relationship and that's a rivalry with Tryndamere). Even his lore makes him seem indifferent to either side of a conflict, since he only desires the conflict itself: "Though these stories remember him as a savior in dark times, Aatrox's true legacy may be a world filled with conflict and strife."
I also consider him to be a graceful swordsman and that sense of grace doesn't really fit with the idea of a tank which tends to be either a large hulking force of nature (think Malphite, Maokai, Bristle[Sejauni], Cho'Gath, etc...), a heavily armored/shielded entity (think Leona, Braum, Nautilus, Blitzcrank, etc...), or a dead/nerve-less entity that can't feel pain and therefore has no problem with eating skillshots and other damaging abilities (think Singed, Sion, Zac). I can only think of a few exceptions like Shen, Vladimir, and Amumu (who really doesn't seem all that beefy).
However, a sense of style and grace is only fitting for Aatrox! An immortal blade-wielding demon-guy has had centuries to perfect his craft! His moves are effortless and sharp! When he uses Massacre he practically glides across the field cutting down foes! His fighting style is very smooth as well with different animations depending on whether it's a normal strike or a Blood Thirst/Blood Price strike. To me it's extremely satisfying to watch him attack.