Flood stories in ancient Mesopotamian literature are a type of cosmogony-creation story. All cultures from that area believed that life and the elements of the universe came from a cosmic sea (there was no vacuum of space in their minds).
One cosmogony does not state that there was a "beginning" in the traditional sense. This particular model claims that life in our current world came from life of a previous world that was destroyed via a flood or collapse of the cosmic waters.
The details differ, but the gods (an essential element or "players" in the cosmogony) either warn a human of the coming deluge who contracts a vehicle to transfer himself and animals from the old world to the present or the gods do the tranfering themselves.
The Noachin flood is the third of three creation-origin stories emoloyed by the Hebrew people in their religious tradition. In it the "sin" of the previous world is wiped out to make room for the new, good, and holiness of the present. In this new paradigm animals are said to fear humans and carnivorous diets as said to begin, but this is due not to sin but due to sin being wiped away by the flood.
Of course the Bible is not saying that the world has seen three creations. The culture from which the Jews emerged shared these three cosmogony models in common, and each was employed in the prologue leading to the "history" of the Jewish people. If you note, the first 11 chapters of Genesis are filled with origin stories, but beginning with chapter 12 the type of narrative used changes dramatically with the call of Abraham. These origin stories are a deposit of the various traditions cherished by the Jews, not a literal history of the world in the chronological order in which they occurred.
The Noachin flood is just the last of the "creations" in this deposit before moving on to address the setting for the actual Torah which begins with the lives of Abraham and Sarah. The eating of animals by animals is seen as a nominal facet of this "new world" without sin after the "flood," but each of the three traditions are backdrops for a more important truth that comes with the Law, not in the creation stories themselves.