Dogs and cats are carnivores and are meant to eat a meat-based diet. I understand that many humans choose to be vegetarians for a variety of reasons, but our bodies are much more suited to this type of diets than our canine or feline companions. Dogs and cats thrive on the nutritional balance that would be obtained from a prey meal – muscle, bone, fat, organ meat, and intestines. Recreating this type of nutrition in a vegetarian or vegan diet is very difficult to do, and I would challenge those that say that they are able to accomplish this feat.
There is a huge difference 
between surviving and thriving. I would be interested to check blood levels for adequate protein, minerals, amino acids, calcium and phosphorus as well as checking for anemia in natural carnivores that are fed a vegetarian diet. I have seen dogs on vegetarian diets and have yet to see one that looks healthy. I have seen dull hair coats, hair loss, flaky skin, along with a general ‘dull’ look in the eyes. The dog may be surviving, but is deprived of optimal health and energy through nutritional deprivation.
In cats, feeding a vegetarian diet is not only unhealthy, but could become life-threatening. Cats are obligate carnivores, there are certain nutrients that they MUST get from meat. Dogs have a greater ability to survive on an omnivorous diet than cats do, but their teeth and digestive system are best equipped to eat meat. The healthiest patients I have seen are those fed a balanced, raw, meat-based diet, with at least 70% of the diet consisting of fresh meat.