Cats and dogs belong to a group of mammals known as Carnivora, and the wild ancestors of both species dined primarily on meat.
Recent DNA analyses indicate that over the course of their evolution, dogs have acquired more copies of the so-called amylase gene, which makes an enzyme that helps to break down starch.
Having more copies of this gene has allowed dogs to eat a more omnivorous diet.
In contrast, the cat family, known as Felidae, lost the genes that encode several key enzymes—including those that manufacture vitamin A, prostaglandins and the amino acid taurine—early in its evolution.
Whereas dogs (and humans) can synthesize these substances from plant-based precursors, cats have to obtain them from meat.
To expand their diet, cats would have to evolve physiological traits that allow them to synthesize these and other key nutrients from plant foods.
This capacity has not emerged during the 10 million years of felid evolution, so it seems unlikely to arise spontaneously in our domestic cats.
From Scientific American - The Inner Life of Cats