Genesis 9:2-3 - "The fear and dread of you will fall upon all the beasts of the earth
and all the birds of the air, upon every creature that moves along the
ground, and upon all the fish of the sea; they are given into your
hands.
Everything that lives and moves will be food for you. Just as I gave you the green plants, I now give you everything."
God gives us permission to eat animals, wonderfully delicious animals. Some vegetarians like to brush this off by saying that was just a very temporary measure, but the fact is that God has never taken that permission away. Rather, our permission to eat animals is re-emphasized throughout the Bible. In addition, he makes us the dominant species.
Deuteronomy 14:11 - "You may eat any clean bird."
God gave the Israelites permission to eat any clean bird. Birds are animals.
1 Corinthians 10:25-26 - "Eat anything sold in the meat market without raising questions of conscience,
for, 'The earth is the Lord's, and everything in it.'"
I realize that the context of this verse is to not worry about whether or not the meat has been offered in sacrifice to a false deity. However, I believe this verse applies both in this context and on its own.
Deuteronomy 12:15 - "Nevertheless, you may slaughter your animals in any of your towns and
eat as much of the meat as you want, as if it were gazelle or deer,
according to the blessing the LORD your God gives you. Both the
ceremonially unclean and the clean may eat it."
One of the key phrases is "eat as much of the meat as you want". You don't need to limit meat consumption for health reasons. Would this verse be in the Bible if a primarily carnivorous diet caused heart disease? For more information, read about the
health benefits of eating meat and the great fraud that is the
Lipid Hypothesis.