From what the poet tells us, it seems that Unferth rather resents Beowulf's appearance in his homeland with the intention of defeating a beast which Unferth himself has been unable to kill. Unferth doesn't want to accept that any other warrior might have done more "glorious deeds" than he himself has done, and therefore, he challenges Beowulf to, essentially, offer his credentials. He accuses Beowulf of having fought Breca out of sheer "wlence," or bravado—pride, rather than pure heroism. Unferth paints a rather unattractive picture of Beowulf, suggesting that Breca got the better of him, and then tells him that he thinks Beowulf will be defeated by Grendel. Unferth seems to be rather jealous. He is used to being perceived as a brave warrior himself, and he resents the idea that another man has been drafted in to do what he could not. Therefore, he is attempting to besmirch Beowulf's reputation.
However, the effect of this is that it offers Beowulf the opportunity to make a heroic boast of his own. He can set right the story of Breca, telling everyone present of his own quasi-supernatural skills, his capacity to hold his breath underwater, and his experience with defeating great monsters. This increases his credentials in the eyes of the gathered men and establishes him as a great hero who is justified in coming here to slay Grendel.