Life can be seen as a journey of understanding and growth. We are born, and until our death we grow and learn. We come to understand the nature of life through our victories and our failures. Although the epic hero Gilgamesh and Homer's Achilles exemplify godlike qualities, great personal power, and loyalty, they both share the same tragic flaw: overweening pride and immaturity. As Gilgamesh and Achilles take on this journey of life, they learn a lesson from their pride and mature heroically.
When we first meet Gilgamesh, the epic's title character, he possesses beauty, strength, and unequaled potential for greatness, but he is a tyrannical ruler, inexperienced and impulsive. The story is about his growth to full maturity as he develops through his friendship with Enkidu and his search for everlasting life.
In almost the entire story of The Iliad, Achilles has been a prideful, jealous, stubborn prick. He is the mightiest warrior in the Achaean army, but he cannot control his pride and his rage makes a puppet of him. He gets jealous of Agamemnon for taking all the glory of winning the battles, which is understandable because he is the one who won them, and withdraws from battle causing much suffering for the Greek army. Achilles doesn't mature until the end of the story when his best friend Patroclus is killed by Hector. This confrontation with the true horror of death brings on the progression of his character from youth to maturity.
In Gilgamesh the gods aren't pleased with the way Gilgamesh has been acting; he's been abusing his rights as king. He exhausts his men in battle and claims the right to sleep with any woman before her marriage. So in order to keep him busy, the gods create a rival for him named Enkidu. This baby sitter that they appoint him symbolizes his childhood through adolescent stages. Gilgamesh and Enkidu go out on quests and foolishly try to kill Humbaba; this strengthens his immature image.