Crimes Against Nature?

This is a little out of the ordinary for me to address a story like this one, but it raised a red flag. NewsOK.com carried a news story entitled Dog sex tapes lead to Tulsa arrest, charges which tells of a women in Tulsa who was arrested for "crimes against nature" which included beastiality. Specifically she and a friend were charged with performing various sex acts with dogs. Let me state emphatically, that I in no way condone this kind of behavior. My question is,

Why is it against the law?

Why are there even statutes on the books that address this kind of
behavior? Is it repugnant? Yes. Is it disgusting? Yes. Is it
stupid? Yes. Is it unsanitary? Most likely. But is it criminal? I
don't think it should be. But obviously it is in Tulsa. I wonder how
many other cities or states have laws covering "crimes against nature."
Apart from global warming and pollution, how do you commit a crime against
nature?

I was especially disturbed that the Tulsa DA's office was recommending that the dogs be "taken away from the suspects and be put down." They want to kill the dogs because the stupid people had sex with them. What possible reason can they have for doing that? This case has ACLU, SPCA and PETA written all over it.