What is Eurylochus' purpose when he says, "I'd rather die at sea, with one deep gulp of death, / than die by inches on this deso
late island here!"? He is trying to convince Odysseus to leave the lost men behind and get off Circe's island before it is too late. He is trying to convince the other men to help him kill a cow. He is trying to rouse courage in Odysseus to face Scylla. He is lamenting his fate while trapped in Polyphemus's cave.
The theme of a story is important because a story's theme is part of the reason why the author wrote the story. The author has a message he wants to share with readers, and he uses his story as a way to get that message across.