You get a pet, which is supposed to be a companion and basically part of your family, and you don’t mind them being torn to shreds?

This is a fair way to feel about it, but if the question is only what is done with a body after it has been euthanized it seems more like a cultural consideration than an ethical one. Like there are cultures with strong feelings about treatment of human corpses to the point where organ donation is taboo, but that doesn't mean being ok with family members being organ donors is some awful thing.

There's a larger question about how pets and other animals are treated, and the thought of someone euthanizing a healthy pet for petty reasons is really disturbing (like stories you sometimes hear about this being done as a way to emotionally abuse someone), but that isn't exactly the fault of the zoo or its practices.