Plankton. If these tiny sea creatures nourish fish and water mammals, why couldn't they nourish us too?
Insects. "Throughout history," says National Geographic, "people have relished insects as food. Today, many cultures still do." The magazine adds that insects are high in protein and pound for pound, require far fewer resources to grow than beef. Marilyn vos Savant once remarked that the insects farmers kill are far more nutritious than the crops they're trying to protect. I won't try to argue with the world's highest IQ.
Grass. We can't actually digest the leaves since our bodies don't produce the enzyme cellulase, but we could take a cellulase pill, couldn't we? Some people take enzymes to digest grains (which are grass seeds) and dairy. Grass covers much of the earth and it's dead easy to grow. Sounds like the food source of the 21st century if people just won't eat plankton or insects.
Organ meat. Could Julia Child be wrong about what's good? Her book The French Chef Cookbook has recipes for liver, brains, kidneys and sweetbreads. Organ meat is also highly nutritious. I'm not a liver lover, but I've sprinkled cooked chicken liver in soup to good effect. A few weeks ago, I bought some calf liver from a farmer's market for my mom, and she remarked that it tasted good and fresh.
I'm not saying you should eat any of these things if you don't want to. My point is that the problem isn't cutting out food groups, it's people's definition of food. I propose defining food as a substance that nourishes and benefits your body when you consume it. If it makes you sick, if you can't digest it without help, it's not food for you.