[periphrasis]

He classifies it as epic poetry, although I don't recall off hand the details of discussion of Achilles, if there even was any. But the Iliad is most certainly a tragedy in its dramatic elements; indeed you simply would not have Athenian tragic drama if Homer and the Iliad were not central to ancient Greek culture. The "Greek Tragic Vision" is Iliadic, and it extends it reach throughout Greek literature, not just the theatrical genre called tragedy: for example, Thucydides' history cannot be fully understood without reference to the tragic vision.

[Cupertino95014]

I think you're walking it back a bit there. You say "What is Achilles' tragic flaw?" in a paragraph about Aristotle. So you did say it.

No question about the centrality of The Iliad though.

[periphrasis]

The point is that Aristotle's views about Oedipus both misread Sophocles' text and fail to generalize across the literary corpus Aristotle was analyzing. Achilles is the quintessential and paradigmatic tragic figure in ancient Greek literature: if Aristotle's insight about tragic character doesn't apply to Achilles, then it certainly makes sense that Aristotle would omit discussing him because such a counterexample so discredits his idea!