In both works, the Classical concept of Arete is fairly well demonstrated. For the Odyssey, pick a moment where Odysseus does not capitulate into fear and fights through adversity, showing his true courage and his greatness for all to witness. The end with all of the suitors and how he strings the bow and then displays his mental and physical dexterity to win back Penelope and his kingdom is fairly worthy of arete. In the Iliad, I would probably select the battle between Hector and Achilles. The former knows that he won't win. He knows this when he offers his son and a prayer for his well- being to Zeus. Yet, despite the cries of his son and Andromache, he goes out to fight Achilles and, in the process, represents the essence of the Greek warrior's notion of arete, where the outcome is secondary to the display of greatness and skill.
Arete is goodness, excellence, or virtue in all things. According to Enotes:
(Greek: ἀρετή; pronounced /ˈærəteɪ/ in English), in its basic sense, means goodness, excellence, or virtue of any kind. In its earliest appearance in Greek, this notion of excellence was ultimately bound up with the notion of the fulfillment of purpose or function: the act of living up to one's full potential. Arete in ancient Greek culture was courage and strength in the face of adversity and it was to what all people aspired.
Excellence in The Odyssey: Penelope says:
My husband foresaw it all, and when he was leaving home he took my right wrist in his hand- 'Wife, 'he said, 'we shall not all of us come safe home from Troy, for the Trojans fight well both with bow and spear. They are excellent also at fighting from chariots, and nothing decides the issue of a fight sooner than this.
Goodness in The Odyssey: Eumaeus says:
Servants never do their work when their master's hand is no longer over them, for Jove takes half the goodness out of a man when he makes a slave of him.
Virtue in The Odyssey: Minerva tells Telemachus:
But mind you never make common cause with any of those foolish suitors, for they have neither sense nor virtue, and give no thought to death and to the doom that will shortly fall on one and all of them, so that they shall perish on the same day.
Excellence and virtue in The Iliad:
The old knight Phoenix says: But mind you never make common cause with any of those foolish suitors, for they have neither sense nor virtue, and give no thought to death and to the doom that will shortly fall on one and all of them, so that they shall perish on the same day.
Goodness in The Iliad:
With these words he sat down, and Calchas son of Thestor, wisest of augurs, who knew things past present and to come, rose to speak. He it was who had guided the Achaeans with their fleet to Ilius, through the prophesyings with which Phoebus Apollo had inspired him. With all sincerity and goodwill he addressed them thus:-
Virtue in The Iliad:
He was son-in-law to Augeas, having married his eldest daughter, golden-haired Agamede, who knew the virtues of every herb which grows upon the face of the earth.