Huh? Meat is simply easier to digest than plant matter. Specifically, herbivores have longer digestive tracts because it takes a long time for THEIR symbiotic bacteria to break down cellulose, which is also "rotting" by your definition.
Grazing animals have extra stomachs to process hardened cellulose. Fruits, roots, nuts and such contain lots of easy digestable nutrients.
The proteins in meat are in general harder to digest than much plant material. (measured in the ratio of the amount of energy it takes to break down the proteins to their amino-acids and other consistants/ amount of energy gain, stored energy in body mass included)
EDIT: I have to add, that comparing cellulose digestion and meat protein digestion is quite out of place here. We humans cook, fry, boil and whatsoever our food, which destroys cellulose membranes and denaturalizes some of the meats proteins (which makes them easier to digest).
That is why we can eat many hard-leafed plants without having extra stomachs, and why meat can be a good source of extra nutrition.
It's the high amount of fat that makes the meat so nutricious in total.
The thing is, the bacteria that decompose meat, have a tendency of being harmful to the body as well. They are intrusive and alien to the body. While the bactreria that reside in our stomach and other intestines live in symbiosis with our body. That's why meat should leave the body as fast as possible.
There is a correlation between eating meat often and colon cancer. (heightened risk through repeated inflammation)