Why do you think Beowulf offers to help a tribe other than his own, in spite of the danger?

The protagonist, Beowulf, in the anonymous,
Beowulf, travels to a distant land to fight a threatening monster
in order to achieve fame and glory.

Like the ancient Greeks
of myth, Beowulf hopes to gain immortality through fame.  His passion is to be
remembered after he dies, and the way to accomplish this is by performing great, heroic
deeds. 

He does say that he's come because it's his duty to
help:

My
people have said, the wisest, most knowing

And best of
them, that my duty was to go to the Danes'

Great king. 
They have seen my strength for themselves. 
(244-246)

And that is
certainly a part of his reason for coming. 

But in general,
Beowulf has his legacy in mind.  He is so worried about his reputation that he even
announces that he will fight Grendel without a sword, since the monster doesn't use a
weapon.  He wouldn't want anyone to think less of him for using a weapon against a
weaponless monster.