Why can cows live on grass but humans can't?

Humans cannot obtain energy by eating grass because the constituents that make up the plant material make it much more difficult for a human to obtain any nutritional value from. Grass is a plant, and it is often a coarse plant that has a rigid structure that contains cellulose, hemi-cellulose, lignin and fibre, all of which impede a monogastric (simple-stomached animal) like the human to properly break down and utilize the energy and nutrients from such a plant. Humans do not have a large cecum like horses, zebras and rabbits do, nor do they have a three or four-chambered stomach like a llama, a camel, a cow or a sheep does. Without these critical organs, humans cannot obtain energy from grass and thus be able to live off of grass.

To shorten this statement up, the simple answer to this question is this: Humans are not adapted to spend a lifetime eating grass. Humans are hunters and gathers by nature, not grazing animals like bison or antelope are.

See the related question for more on the ruminant physiology side of eating and digesting grass.