What good reason would there be for feeding a dog a vegetarian diet?

why not... aren't dogs omnivores?

if the dog is allergic to 'animal proteins'
i think that's a pretty good reason.

I have a dog with a medical condition that I tried it with. She did not do well while on it and vomited on and off the entire time she was on it. I changed her to the reduced fat,same company, and she is doing really well.