If you want to take a biblical view on this - Man was given dominion over the beasts of the earth. However, in Genesis 1:29 god only gave man plants to eat:
And God said, “Behold, I have given you every plant yielding seed that is on the face of all the earth, and every tree with seed in its fruit. You shall have them for food.
It wasn't until after the flood (Genesis 9:1-3) that god gave man permission to eat the animals.
And God blessed Noah and his sons and said to them, “Be fruitful and multiply and fill the earth. 2 The fear of you and the dread of you shall be upon every beast of the earth and upon every bird of the heavens, upon everything that creeps on the ground and all the fish of the sea. Into your hand they are delivered. 3 Every moving thing that lives shall be food for you. And as I gave you the green plants, I give you everything."
So there is argument for veganism in the creation but argument for omnivorism after the great destruction.