We have given certain animals the designation of being "food animals" therefore it is okay to eat them
It's meaningless to simply assert that it's okay to harm certain animals because we said so. What is the significance of saying "This animal is for food, this one is for tying in my basement and whipping for my enjoyment, and this one is for my sexual pleasure."? Could we simply assert that any animal has any purpose and it's suddenly morally acceptable to do whatever you want to it?
Furthermore, does this work for any species? Could I assign some baby dolphin in shallow water on the beach the role of "animal that is intended to get its fins cut off and thrown back into the water so I can watch it suffer for fun"? It would seem pretty obvious that this a very weak argument for doing unethical things to animals, simply because we can just slap on a label that says "This is ethical because I said it's ethical. Therefore it is ethical."
"Sorry I stole your car; I assigned it the purpose of theft". "Sorry I murdered your daughter. I assigned her the label of murderable human". These are just so obviously absurd in any other context. This is no different.