>why was every story in the ancient world written as a poem?
They weren't.

>was there some reason it all had to rhyme, or was that just the best way to kill time or something
Well in Homer's case the poetic rhythms would have helped to memorize the story, it all going back all the way to Proto-Indo European.

>did people writing non-fiction, like Thucydides and aristotle, write in some rhyming verse?
I don't believe Thucydides did but Aristotle or Plato might have.