Perhaps the greatest example of Achilles fighting skill is when he fights with and kills Hector, the greatest of the Trojan warriors. However, this fight may have never happened if Athena had not disguised herself as one of Hectors brothers and convinced him to fight. Achilles fails miserably at respecting anyone in authority, whether governmental or religious. He not only disrespects King Agamemnons authority, but also the goddess Athena herself. This lack of respect begins when Achilles calls an assembly of the Greeks, something only Agamemnon was able to do. He then proceeds to insult the king, telling him he is greedy, shameless, a cheater, and a drunk. To top it off, Achilles contemplates drawing his sword to strike down Agamemnon, and is only stopped by Athena grabbing his hair. Needless to say, killing the leader of your nation would be the ultimate act of disrespect to the government. Although he does so badly with respect for government authority, Achilles has no problem respecting human religious authority, only because he has no encounters with priests, prophets, and etceteras. However, he does show some disrespect to Athena for stopping his murder of King Agamemnon. Instead of following the goddess orders whole-heartedly, he does it quite reluctantly and talks back in the process.
Humility is another requirement Achilles fails to meet. His excessive pride is seen throughout The Iliad. When he tells Agamemnon that he is withdrawing himself and all his forces from the Trojan War, Achilles makes it sound as if he has done greater things than anyone, putting himself on a pedestal. Never does Achilles credit anyone or anything for his success, including the gods. It is always he himself who has done something. Although Achilles is so prideful about his deeds, he is able to accept Fate. As he reprimands his horses as if it were their fault Patroclos was killed, one of them tells Achilles his death is near. Achilles tells the horse he knows this, indicating he accepts it. Hector does not credit himself for his accomplishments. He usually gets around glorifying himself by thanking the gods. Achilles pride contributes to his downfall, and it also shows Hector to have far less hubris than his opponent.
Composure may be the requirement Achilles is furthest from meeting. Almost every time his name is mentioned, he is in some fit of rage. His very first tantrum is when he about kills Agamemnon, only being stopped by Athena. His next episode of anger comes after the death of Patroclos, but it is actually helpful to the Greeks. Achilles charges over the battlefield, destroying all Trojan warriors he crossed paths with. The final act of Achilles great anger is after he kills Hector. Achilles is still deeply hurt by the death of his friend Patroclos, so he drags Hectors body behind his chariot, mutilating it.
The Epic of Gilgamesh embodies the national ideals of the Sumerians who believed that coming of age of a young man especially one who would become king, required a ritual experience. That aided the young man to face his monsters, nature, gods, and the reflection of Gilgamesh found in his mirror image Enkidu. The Sumerians understood the need for such a quest of self because there is a person that resides in all of us, both benefactor and destroyer that must be identified and controlled before we can accept our adult responsibilities. This is why the story incorporates emotions, but they are also unrealistic. Gilgamesh must face his anger and learn to replace it with a sense of community that is much closer to love, not hate. His ego must also be trained to respond appropriately to both winning and losing because this is what life is for each of us.
The ancient Greeks had strict criteria for individuals to follow if they were to be seen as heroes. Those requirements were skill in battle, respect for authority, humility, and coolness under fire. Not many men met all requirements, including Achilles and Gilgamesh, but they were still viewed as heroes. When the emotions are brought under control, when each person is successful at slaying their "dragons," then they can move into an adult position that requires control over all the dualities of love and hate, power and weakness, anger and joy, selfishness and community. Between Achilles and Hector, Hector was the better choice for the title of hero, he was respectful of authority, humble about his success, and was very levelheaded. Achilles had great fighting skill as well. However, he had trouble respecting authority and keeping his cool, both results of his excessive pride. If Achilles had not been so prideful, he could have been a much greater warrior and hero, perhaps achieving status equal to the gods. He simply had too much pride. As desired, Gilgamesh learns to do good deeds, and this is truly all that society asks of anyone.