Beowulf comes to fight Grendel to help King Hrothgar, whose great hall Heorot has been terrorized by the monster Grendel. Beowulf, a hero of the Geats, hears about Hrothgar's troubles and, with his king's permission, leaves his homeland to assist Hrothgar. Beyond this heroic duty, Beowulf's journey is also tied to a sense of loyalty and repayment: Hrothgar had once helped Beowulf's father, Ecgtheow, by paying a wergild or blood money to settle a feud, thus saving his father. This act creates an obligation that Beowulf feels compelled to honor. Furthermore, Beowulf seeks to prove his strength and bravery, aiming for fame and glory through the heroic deed of defeating Grendel. He notably fights Grendel unarmed, believing himself Grendel's equal and engaging him in hand-to-hand combat to protect Hrothgar's people and halls.
In summary, Beowulf's reasons for coming to Hrothgar to fight Grendel are a blend of repaying a familial debt, fulfilling a heroic obligation, and seeking personal glory through a courageous and self-imposed challenge.
