King Hrothgar was in disgrace. Grendel, a demon and descendant of Cain had been assaulting Heorot for years, taking the people that he as king was sworn to protect essentially right from under his guard and care.
The situation had become so dire that the Danes had even forsaken God and had taken up idols and called on the devil hoping for some relief from their problem.
Basically, for Hrothgar, defeat of Grendel was everything to him. He had lost his honor, his kingdom, and his faith...and he and his people were all completely at the mercy of Grendel and, unless Grendel could be defeated, all of these were completely lost to him.
So basically, if everything that defined both your physical and spiritual self were wrapped up in the defeat of a being, it would probably be rather important for you as well.
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The defeat over Grendel was important to King Hrothgar because it brought peace and safety back to his kingdom. Grendel had been terrorizing the people of Heorot, causing death and destruction, and the defeat allowed Hrothgar to regain control and restore order to his land. It also boosted his reputation and reaffirmed his authority as a strong and capable ruler.
Because Grendel was like a curse and shame to King Hrothgar. And think about how much disaster he was causing for years!