First thing, of course, ensure there's no medical or physical reasons for your cat or dog's reluctance to eat. If there are other symptoms, such as lethargy, vomiting, mouth or gum sores or bleeding, etc, please consult a veterinarian.
Just like humans, cats' and dogs' appetites can be affected by external factors. They may be responding to some kind of stressors in their environment, sometimes entirely unknown to you. It could be a simple change in temperature. Some dogs are less interested in eating when it starts getting hot outside. Many dogs have seasonal allergies and may not want to eat when pollen season is in full swing.
If your dog is an older puppy or young adult, it could be that he or she has entered the adolescent developmental stage where psychological and hormonal changes are happening. Just like in human teenagers, they may exhibit rebellious behaviors such as not wanting to eat or being overly picky about eating.
Dogs and cats may also be stressed by changes in their home environment and might need some time to adjust. All of these reasons are temporary and will pass. If you're concerned about them getting nutrients, our goat milk or goat colostrum are excellent sources of vitamins and nutrients.
If you've recently changed food, it may simply be a response to not getting what they were expecting. They may refuse to eat, in hopes the food they're used to eating is provided. Usually once they understand that the other food isn't coming and this is it, they'll eat it and after a few times, the new food becomes the new favorite. If you have some holdouts, we've found green lipped mussel powder to be very effective in encouraging eating, especially with cats. Break open a capsule and sprinkle it on the food.