I wouldn't say that Beowulf's boasting shows him to be offensively arrogant. In the ancient heroic times of Britain, boasting was a sign of strength and bravery, and Beowulf had to boast to show others that he is a hero deserving of his title. Nobody thinks of him as an arrogant person but rather a savior. Today, I guess you could compare his boasting to writing a resume - there, it is your job to practically 'sell yourself' by promoting your strengths in order to get the job you want.
