Ok, but this conclusion is not just from the Song of Achilles. This is in fact the conclusion that we as readers are supposed to come up with as we read the Iliad. What is more, the Song of Achilles merely misquotes an actual line that Achilles says to Hector before killing him: “I wish only that my spirit and fury would drive me to hack your meat away and it raw for the things that you have done to me.” (Lattimore, The Iliad of Homer, book 22 lines 341-343). But even without this line, even without the promise of actually eating human flesh, the Iliad does a very good job of showing the reader that Achilles has lost his humanity due to grief.
There are two aspects of Achilles in the Iliad. Before Patroclus dies, Achilles is mainly concerned with his own renown and honor ( κλέος and τιμή ), and so, when his honor is slighted, he refuses to fight. This is his human side. Since Achilles is mortal and will die, his only claim to immortality is the honor given to him and the renown that will live on after him. By taking away his war prize and honor, Agamemnon effectively takes away the reasons Achilles has to fight. As a warrior, a human, Achilles cares most about his own honor. This can be seen before Patroclus goes off to fight too, when Achilles says to him: “you must not set your mind on fighting the Trojans, whose delight is in battle, without me. So you will diminish my honor.” ( Lattimore, The Iliad of Homer, book 16 lines 89-90)
That was the first aspect, the second is after Patroclus dies. When Patroclus dies, human concerns don’t matter to Achilles anymore. As grief envelops him, Achilles ceases to eat and sleep, he ceases to hold his grudge against Agamemnon, he fights a river, he slaughters armies– “food and drink mean nothing to my heart but blood does, and slaughter…” ( Lattimore, The Iliad of Homer, book 19 lines 13-14). In his grief and rage, in his refusal to eat for example, we the readers see that Achilles no longer behaves as humans should, but instead, as immortals do. Achilles breaks almost all human convention because of his grief, to the point that even the gods notice. His behavior is supposed to jar us, to let us see that humanity has departed from Achilles. The line he says to Hector saying that he wishes he could eat him, merely points out how far gone Achilles is, and how inhuman, but he is not immortal, and therefore, cannot eat another’s flesh.
This disregard for human customs and necessities means that Achilles’ death will come, he can’t go on behaving unlike a human forever. He knows he will die, and does not care. The moment Patroclus died, Achilles did so as well, in a sense. If death is to come to him, why shouldn’t Achilles behave like an immortal? He no longer cares for anything but revenge, and once revenge has been achieved and his unhappiness does not stop, he cares for killing other Trojans and reliving his revenge by attempting to defile Hector’s body. Achilles has lost what mattered to him most, which in the end, was not his glory but his Patroclus. It’s only after Priam appeals to him as a father and reminds Achilles of his own father Peleus, that Achilles regains some semblance of humanity.
So, in fact, the Iliad shows us that Achilles has lost his humanity, that he lost it after Patroclus died. It shows us the limit of his loss, in that he cannot eat the flesh of Hector, and it shows us that human concerns (honor and glory) cease to matter to Achilles after Patroclus dies. It does so much more subtly, but it does show it. It’s one of the biggest concerns, in fact, of the latter books of the Iliad.