Why does Beowulf have to kill Grendel?

Beowulf states that he will fight Grendel without armor or sword, hand to claw, because the ogre does not use weapons. If Beowulf is killed, he wants his war-shirt (breast armor, mail) returned to King Hygelac. Hrothgar offers a joyful feast in honor of Beowulf's arrival.

Their battle concludes with Beowulf's ripping Grendel's arm off, fulfilling his promise to Hrothgar to kill the monster with his bare hands. Beowulf nails Grendel's severed arm to the mead hall rafters and, although Grendel runs away, he is later found to have bled to death in his underwater lair.