Arrogance as defined by WordNet means: overbearing pride evidenced by a superior manner toward inferiors. This defining character trait can be seen throughout the Iliad and its ability to seize and control the mind is quite poignant.
In the Iliad, it is quite obvious that Achilles, Agamemnon, and Hector have the greatest arrogance out of all of the major characters. This arrogance is not only a sense that you are better than someone else but that you can never be wrong and to question your ideas or actions would be dangerous. In the case of Achilles, his arrogance has lead him to believe that he has no reason to be fighting against the Trojans. He believes that he is better than Agamemnon and that he will only fight when Agamemnon has admitted he has made a mistake regarding their relationship. Achilles is only rallied to fight and reconcile with Agamemnon when Patroclus is killed by Hector. Only after this happens is Achilles able to put aside his arrogance and quarrels and fight alongside Agamemnon.
In Agamemnon's case, his arrogance is much like Achilles. He believes that he is never wrong and that his decisions should never be questioned. As we stated in class, a great leader should posses qualities such as honesty/charisma/wisdom, and most importantly, the ability to recognize errors. Because of his arrogance, Agamemnon has a hard time recognizing his selfishness in taking Achilles' prize (Chryseis). His inability to even compromise with Achilles shows a lack of honesty and more importantly, wisdom. How can Agamemnon believe that he is the greatest king while still making such crucial mistakes? The answer is arrogance. It seems that, at least in Agamemnon's case, that in order to be a great leader you must NOT have a sense of honesty or directness or even an ability recognize errors. Although I disagree with this claim, it seems quite valid in terms of the Iliad.
Finally, in Hector's case, his sense of arrogance has been growing as of late. Although, it seems, in order to be a great leader, your greatest attribute must be arrogance, Hector has only displayed it recently. More importantly, he has only displayed it with such intensity after he has killed Patroclus. Although I am not trying to say that Hector was arrogant before killing Patroclus, it has been more evident recently. Killing Patroclus instilled in Hector a sense of arrogance that he will never be able to see past. In the fury of battle, Hector's arrogance grows and is displayed most when he takes responsibility for killing Patroclus. He believes that he did the act alone and cannot reconcile with the fact that Apollo and Zeus played a role in Patroclus' death. Much to the dismay of the Trojans, Hector takes the armor of Achilles off of Patroclus' body and does not follow the agreement of allowing the dead their rights. Fortunately, for Achilles, and for the Achaeans, the armor has only one true bearer, and it eventually turns against Hector and curses him, as if it has a life of its own.
In all three cases, it is important to note arrogance as a defining character trait. Arrogance is the worst trait to posses, and the three most important characters posses a copious amount of it.