For the most part, we recommend feeding against table scraps because it keeps the diet simple and easy to control if we follow the rules of well planned, raw, species-appropriate diets.
DOGS: If your dog has any health issues, we strongly recommend against feeding scraps. The best chance we have of helping you improve your dog's health lies within a tightly controlled diet plan. Any inappropriate nutrients or ingredients can be enough to cause a very annoying set-back. For example - a dog with sensitive skin may be doing really well on their novel protein diet, until someone gives them a crust from their toast, and suddenly the dog is super itchy again.
Wild dogs often have robust constitutions. Domesticated dogs have been subject to many of the same pressures (highly processed foods, antibiotic overuse etc) that have correlated with the rise in allergies and chronic disease in humans. Our pet dogs may be less able to thrive on a diet that includes some scavenged food, compared to their wild counterparts.
If your dog is very robust (no gastro upsets, no itchy skin, so other health issues) and you make the decision to feed them some scraps - please be very selective: make scraps a small part of the diet. Some human foods are toxic to dogs (such as onions), and some are dangerous (cooked bones - the dog on the right in the picture could be in serious trouble if he were to eat that chicken!).
CATS: Cats are very rarely interested in table scraps. And being true obligate carnivores, table scraps are seldom suitable. They are unlikely to provide any nutritional value to your cat.