Super heroes? The characters from Greek legends are often deeply flawed. Achilles, the fleet-footed mankiller, may be a great warrior, but he is also the guy dragging the body of Hector, Patroclus' killer, around Troy out of revenge. Heroes (in the classical sense of the term) are very different from "heroes" as we understand it. They are larger-than-life figures, rather than embodiments of desirable qualities.
Those are surface flaws, designed to give the appearance of wrongdoing. Despite how heavily Batman's internal struggle is emphasized, he never does anything less than noble. Contrast that to Achilles' treatment of Hector, which even in the context of ancient Greece is presented as being beyond the pale.