How is each of the mosters anathema to the Anglo-Saxon culture?How do the monsters of Beowulf stand in contrast to Anglo-Saxon values?
The Anglo-Saxon culture valued honor, wisdom, generosity, and loyalty. The monsters in Beowulf are the antithesis of these ideals (with the possible exception of Grendel's mother.)
Grendel is obsessed with hate for all thing good and pure. Because of this passion, he destroys anything associated with valor and courage and joy--beginning with the brave warriors who served Hrothgar.
Grendel's mother, while she displays some sense of the values of loyalty and vengeance (she does, after all, seek to restore her son's "dignity" by removing the trophy of Grendel's arm from Heorot), hoards the treasures of those she had destroyed. This, of course, leads to her destruction because Beowulf uses part of her hoard to kill her.
The dragon is also an antithesis to the values of loyalty, kindness, and generosity. The dragon contains the worst of both Grendel and his mother. The dragon hoards his treasures and when a desperate slave steals one small item the dragon, rather than show mercy, retalitates by terrorizing the whole country. This dragon did not destroy only those responsible for his anger, but the innocent as well, making him the most reprehensible of all.