He wanted to deal with Grendel single-handedly because he was "the hero". Grendel is no braver, no stronger that I am I will meet him with my hand empty." These words made the people of Herot certainly think of Beowulf as an epic hero, and he got what he wanted after he showed his great strength in killing Grendel - fame, and becoming immortal in the minds of his people. Beowulf was like a young child who purposely puts his fingers into a socket, gets himself in danger, so he could game his parents" attention and concern. .
Beowulf, when returns from the victory by the slaughtering Grendel's monster mother, he doesn't bring back anything else except for Grendel's head back to the hall. "The monsters" hall was full of rich treasures, but all that Beowulf took was Grendel's head." Beowulf was an epic hero who did care about his people, but the task of fulfilling his desire of receiving fame from them was the first on his to-do list. He could have taken all the gold he wanted for himself, or at least for the people of Herot, yet his materialistic mind only brought back the head of the gigantic Grendel, the monster, which Beowulf cut off in "a single swift blow." .
When Beowulf realized that because of his people the dragon is burning the city, Beowulf could not turn his back at them because it was the question of keeping up to his fame. Beowulf goes ahead to deal the deadly, dangerous dragon. It could be argued that Beowulf first thought about himself, and then his people because he actually did go and fight the dragon. Him being the king, he should have realized that he could be killed by the dangerous dragon especially because he wanted to fight the dragon alone even though his age was 70, not keeping in mind the consequences of the Geats if they lose their king. The thought of being immortal didn't leave him till his last breath. He told his follower, Wiglaf, to build a tower to his name, and to spread his good deeds.