One major reason is that Grendel was likely descended from Cain, the son of Adam and Eve who killed his brother Abel in a spiteful rage. For this sin, God punished Cain and his descendants, causing them to be filled with anger and hated wherever they went. This is alluded to in the text:
For that bitter murder,
The killing of Abel, all-ruling Father
The kindred of Cain crushed with His vengeance;
In the feud He rejoiced not, but far away drove him
From kindred and kind, that crime to atone for,
Meter of Justice. Thence ill-favored creatures,
Elves and giants, monsters of ocean,
Came into being, and the giants that longtime
Grappled with God; He gave them requital.
(Hall, Beowulf, gutenberg.org)
This stigma would cause Grendel to be bitter, not only for his own lot in life, but moreover to see the people around him who are not suffering from this curse. It is stated that Grendel listens to the sounds of Hrothgar's mead hall for a full year before he attacked it; Grendel is filled with envy for the "normal" people in the world who are not stigmatized and allowed to pursue their dreams. Grendel, though, is destined, almost forced, to live a life of sin and hatred; his understanding of this would fill him with anger not only at the people around him, but at God for giving him this undeserved destiny. Instead of striving to change it, then, Grendel embraces his role as villain, and is destroyed because of it.