Beowulf wants the public to realize that Unferth is not a person to be listened to and taken seriously for his questionable actions.
In "Beowulf" we are introduced to the character Unferth, who wants to have honor and fame in the realm, as Beowulf. When we read this character, we can infer that:
Beowulf is not happy to discover the rumors about him and so he tries to show everyone that Unferth is not a trustworthy man and that he doesn't deserve to be listened to, because besides not being a hero, he did questionable and even cruel things like killing his own brothers.
It's important to remember that "Beowulf" is the Anglo-Saxon tale, which tells the story of how the hero Beowulf managed to kill terrible creatures that plagued people.
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