Why is killing Humbaba important for Gilgamesh and Enkidu in The Epic of Gilgamesh?

Gilgamesh, befitting his epic hero status, wants to fight and kill Humbaba to prove to his people that they should not be afraid of Humbaba and that the gods are able to be defied by mere mortals. Also, perhaps as a secondary motive, he wants to be able to inspire the youth of Uruk with his mighty deeds to encourage them to be great and powerful in the same way that he is. Note what he says in the following quote:

I want to prove
Him not the awesome thing we think he is
And that the boundaries set up by gods
Are not unbreakable. I will defeat him
In his cedar forest. The youth of Uruk
Need this fight. They have grown soft and restless.

Gilgamesh therefore openly states that part of his reason for wanting to fight Humbaba is to confront the fear that his people have of him as an "awesome thing" and also to challenge the gods in setting up their boundaries, which mortals think are "unbreakable." Of course, these motives, with their arrogance and hubris and defiance, are completely fitting for an epic hero who is determined to make a name for himself by doing what others do not because they are too afraid.

Why did Enkidu want to kill Humbaba in the Epic of Gilgamesh, and why was Gilgamesh reluctant?

Humbaba (Akkadian spelling, Huwawa, Sumerian) is a monster appointed by the weather god Enlil to guard the Forest of Cedars. In Tablet I he is described by Enkidu as:

　''When he roars it is like the torrent of the storm, his breath is like fire, and his jaws are death itself. He guards the cedars so well that when the wild heifer stirs in the forest, though she is sixty leagues distant, he hears her"

　In Tablet II:

　"Humbaba’s roar is a flood, his mouth is death and his breath is fire! He can hear a hundred leagues away any [rustling?] in his forest! Who would go down into his forest!"

　Essentially, the character of Humbaba is that of an inimical force of nature, personified as a terrifying giant combining the characteristics of beast and man magnified to superhuman size.

Initially, Enkidu is restless in Uruk, and thus the quest. Gilgamesh initially is frightened, but Enkidu encourages him. Next, Humbaba offers Gilgamesh all the cedars and himself as a servant, but Enkidu (1) wants the fame and glory of killing him and (2) insists that if they do not kill him quickly before the gods arrive, the gods will intervene and prevent the death of Humbaba and destruction and looting of the sacred trees.