Is Beowulf Selfish?

I think Beowulf is being selfish. He wants to make up for his father's mistakes by killing the demon that has landed on the same grounds his father "had begun abitter feud" on (37). Beowulf wants his family name cleared and believes he is strong and courageous enough to clean the slate. However, everyone wants a little fame in their lives, and Beowulf just happens to be going through this stage of his life when Grendel appears. He "longed only for fame" (71), and felt he could not live without it. The thought of being famous drove him to become brave and fierce enough to fight and defeat the demon. An entire land praising him and believing he was a true hero was all that Beowulf needed to satisfy his demands, and that is exactly what he got. And once Beowulf defeated Grendel's mother, his demands were satified to the extreme. "And I promise you that whoever sleeps in Herot...they, and you may now sleep without fear of either monster, mother or son" (75). His two defeats rose Beowulf's spirits and he now feels he can defeat anything or anyone that steps in his path.