This is an interesting question. Book 9 is a major turning point in the story. We read about Agamemnon finally apologizing and sending gifts to Achilles (including the return of Briseis, the slave girl), asking him to come back and fight with the Greeks so that they can defeat the Trojans. Achilles refuses his gifts, though, saying that he will not return to help the Greeks until Agamemnon is grovelling on his knees before Achilles. Achilles isn't behaving very much like a hero - rather, he's continuing to act like a spoiled little boy whose toy (Briseis) was taken away.
So, to look at this from Achilles' point of view - I would say that he is very short-sighted in his view of the heroic system. He would rather fight and die in battle than stay at home and die an old man in his bed...yet, what is he doing? Staying behind in his tent, pouting, while the Greeks are struggling to survive in the war.
Perhaps a flaw from his point of view would be the fact that they are all operating under the assumption of honor - that as Greek heroes, they will act with honor. When Agamemnon does not, it throws a major curveball at Achilles, and so he responds with less than honorable behavior himself.
Check the link below for more information. Good luck!