To illustrate this point further: a few examples of characters whose undoings can appropriately be called tragedies. Oedipus: undone by his own intelligence and effectiveness at doing his job as the ruler of his city. Beowulf: becomes a king through his merits as a hero, then dies and fails his kingdom because he can't stop trying to be a hero. Hamlet: a scholar who thinks too much for his own (or anyone else's) damn good. Neil Gaiman's Morpheus: would rather die than change. Scarface: a modern-day Richard III, brought low by the ambition and reckless courage that drive his rise to power and make him such a likable character. You want examples from video games? How about General Leo, whose chivalry and honor get him killed? Once he gets on his knee when Kefka reappears disguised as Gestahl, you know Leo has just dug his own grave. And Andrew Ryan: can he do anything but die after his principles – of which Rapture is a physical manifestation – completely backfire on him?
Notice a pattern? There is a certain undeniable sense of inevitability underlying these characters' stories. The qualities that make them great, make us like them, and make them who they are ensnare and destroy them. There is always some pivotal final decision on their part which ends up dooming them, but in almost every case, who they are incapable of choosing anything else. They string their own nooses, and that's what makes it tragic. But Aeris? She just gets blindsided by some silver-haired maniac whose motivations are anyone's best guess at that point. You can say Aeris's death is sad, moving, shocking, troubling, heavy, lachrymose, or grievous, BUT DON'T SAY THAT IT'S TRAGIC, BECAUSE IT ISN'T. CEASE DEGRADING THE TERM AND STOP MISLABELING AERIS'S DEATH.
Thank you. Glad to finally have that off my chest.