Early in the final book of Homer's Iliad, the god Apollo criticizes the other gods for allowing Achilles to defile Hector's corpse by dragging it behind his chariot. Apollo argues that Hector had always honored the gods with sacrifice and now his corpse is being defiled. Apollo goes on to say that Achilles is behaving like a wild animal and that
"Achilles is as devoid of pity, and of the shame that benefits men, urging restraint." (A.S. Kline translation)
Thus, it appears that the sort of shame Apollo describes is that which restrains a person from behaving in a manner that would be displeasing to the gods. By defiling Hector's corpse in this brutal way, Achilles is acting in an unrestrained manner. Such disregard for common decency is probably what the Greeks would label as hubris. In Greek mythology, committing an act of hubris will almost always result in a person being severely punished by the gods.
The sort of shame that Achilles should be exhibiting is an attitude of respect for the notion that all people deserve a proper burial after they die, even a person's enemies (compare Sophocles' Antigone).
There is always shame involved when men are unable to decide positively upon their differences, or allow themselves to differ and remain unhurt. The weak and negatively debase structure of man is shame - and has been since the beginning of time. When Adam and Eve were separated from their Father in Heaven because of their shame in nakedness, a form that began as beautiful in the eyes of God, they sewed fig leaves together to cover their beautiful bodies, in shame. They hid from their Father because they were ashamed. Man has destined himself to face shame because of his sin. Shame hurts men because it was never their destiny to have shame enter their lives. The future of their good fortune and prosperity in life is ruined because of the shame they face. When men hate other men so much that their deaths are the only recourse, it hurts men and generations of men because shame will carry them throughout eternity. The shame of ones actions buries itself deep in the heart and the spirit and that shame is carried upon the generations of sons and daughters. Only the brave and strong and the elite in love can see shame as a tool and turn away from it, never to allow its light to shine again, nor its spear to pierce the heart of hearts.