Zeus was the chief figure in the pantheon of Greek gods who lived on Mount Olympus and created enough drama to fill a thousand years worth of television soap operas. When the gods wanted something, there was nothing to hold them back from taking it. According to Greek mythology, if a god wanted to curse you or kill you for no reason at all, there was nothing you could do to fight back. Similarly, as detailed in myth lore, if a god fell in love with a pretty girl or boy walking through the woods, they had no qualms about descending to earth disguised as an animal to take the object of their desire by force. Shakespeare's character Edmund from King Lear had this conception of the gods in mind when he said: "As flies to wanton boys are we to the gods."
Zeus is an anthropomorphic figure in Greek mythology – his behavior is modeled on human behavior – but once he becomes a swan, he is incapable of expressing human emotions. His indifference at the end of the poem shows him to be a symbol of the impersonal forces of nature, like the oceans or the weather.