I wish this was more complicated, but it's not.
Realizing the above we begin to picture, in our mind's eye, some interesting things. As you read the following, think of cows, horses and/or goats and how they eat. At the same time, think of how lions, tigers, wolves, coyotes, leopard, etc eat — if you have never seen these animals eat, watch a wildlife documentary.
Let's start with the herbivores. The herbivores are grazers. They have a small stomach and thus they must eat small amounts but often. Thus the reason why herbivores are constantly grazing. Now, since vegetation takes longer to digest that animal protein (meat), herbivores have an exceptionally long intestinal tract so their body can more fully digest and break down the vegetation.
On the other paw, we have the carnivores. A carnivore eats meat and because prey is hard to catch than the grass the herbivores eat, the carnivores eat a big meal once they catch their meal. Let's face it, prey can run away but grass cannot. When you think about it, herbivores have it easy because their food doesn't run away.
Okay, so when the carnivore catches its prey, it knows it had better eat a lot because the carnivore does not know when it will catch its next meal. So the carnivore eats ton of food — sometimes the carnivore eats so much food that it can't move after eating. I've seen wildlife documentaries where the lions, after eating a zebra, have such a plump stomach that the literally cannot move when the safari group passes by. In fact, carnivores have been known to eat as much as 25% of their own body weight.
But getting back to our carnivores. Realizing their stomach is 65% of their digestive system, they eat a huge meal. Realizing that animal protein (meat) requires less time for digestion than vegetation, our carnivores have a very short intestinal tract because their body digests the food fast and then eliminates the meat quickly before any putrefaction can begin within the intestinal tract.
Now, if you were to feed meat to a herbivore, then due to the fact their intestinal tract is so long, the meat would stay in their body too long causing putrefaction. Conversely, if you feed whole vegetation to a carnivore then the vegetation passes through their short intestinal tract before it can be fully digested causing the vegetation to magically reappear in their stools.
This is why, briefly, grains are not good for carnivores and meat is not good for herbivores.