The problem with trying to convince someone of something is that they have to WANT to be convinced. You need to "sell" them on the reasons why they would EVER want to give up bread, pasta, desserts, rice....all that "good" stuff. Seriously, grains are such a part of most people's lives that they literally can't picture how they would manage without them.

Despite the fact that all the other posters have posted great (and quite valid) suggestions, I would think that the most effective elevator speech would address that person's own problems. What is it that THEY are looking for? Do they want their food to be "natural," or do they have digestive issues, immunity problems...do they want to have better breath, cleaner hair, fewer illnesses? Customize your "elevator speech" to their needs and you will have a 300% better chance of convincing them. Don't tell them how BAD wheat is. Tell them how GOOD life is without it (yes, I know that's not actually what you asked for). Realize that you are going to have to talk about this more than once.

Your first step should be to just get some interest going. I can't tell you how many people have zero interest in talking about food or health, and certainly not evolution :-) Keep coming back to the subject but just don't give the appearance of trying to push anything on them. Remember: in order to have any possibility for success, you have to make it attractive to them. And then, be ready for the fact that once they do it, they are going to think it was all their own idea :-)

Most people's eyes will glaze over if you mention any kind of science. Remember, wheat (specifically wheat germ agglutinin or WGA) has addictive properties, and binds to the opiate receptor in the brain (the same receptor heroin and morphine bind to). Would you try to use science or reason with someone who's addicted to painkillers? Nope, because they're just not going to hear it. (This is an extremely simplistic metaphor).

What I always tell people is that I didn't know I was unhealthy until I removed wheat from my diet and it made me feel a lot better. I saw improvements in X, Y, and Z, etc. People are always more responsive to personal stories that center on you, rather than scientific arguments that just make them feel judged and unworthy, and consequently, very defensive.

Eliminate wheat and you will find, blood sugar drops to normal, blood pressure drops, triglycerides drop by several hundred milligrams, HDL goes up, small LDL plummets, c-reactive protein drops. Improved rheumatoid arthritis, Improved ulcerative colitis, cramping, and diarrhea of ulcerative colitis, can experience marked improvement. Reduction or elimination of irritable bowel syndrome. Reduction or elimination of gastroesophageal reflux. Better mood. wheat is responsible for a subset of schizophrenia and bipolar illness. Better libido. Better complexion. Wheat increases hunger dramatically. Wheat is worse than table sugar in triggering a rapid, large rise in blood sugar. Autoimmune diseases--Most notably celiac disease and thyroiditis.

If a vegetarian tried to make an elevator pitch to me about why meat is bad for me I'd be seriously pissed. I think the same goes for trying to convince people not to eat wheat unless they are already receptive to the idea and initiated the discussion. If they did want to hear the reasons why, I think I'd say we're not ruminants and therefore eating grass is not conducive to our health and there are far better alternatives that have superior nutrient profiles without the toxins. The idea of not eating grass seeds is what convinced me that Paleo made sense.

Tell them if they were to go out into a wheat field, and "eat wheat" out of the field for a meal, they would probably die.

The amount of processing needed to make wheat edible in current form today is truly amazing.

Why (10,000 years ago) did people even got through the trouble of harvesting and processing wheat? It never made sense to me.

Anthropologists can look at an ancient skeleton and tell you immediately whether the person was from a hunter/gatherer group or a farming community, because when man began to farm grains, he got much shorter and developed all sorts of teeth, bone and other ailments not seen in hunter/gatherer populations. Plants like wheat produce harmful substances in their seeds to discourage animals from eating them. We are not biologically adapted to thrive on wheat; one meal won’t kill you, but over time, serious problems can arise. [insert personal testimonial here]

I like to tell the story of the Paleolithic grave found in North Africa with skeletons of the Kiffians as tall as 6'8" (all adult skeletons were at least 6'0), thick bones which indicates muscle, strong healthy teeth and no signs of the diseases of civilization. This was during the "green phase" of the Sahara, about 9,000 - 10,000 years ago.

This same grave was also used by later Neolithic herders/farmers called the Tenerians just a few thousand years later. They were a lighter people, the average height in this later grave was 5'5" with all the diseases of civilization ...

BTW, a few months ago there was a story on research done ancient Egyptian mummies and how heart disease and other diseases of civilization were found in the remains. The conclusion was that ancient people had all the illness we do. What wasn't mentioned was the ancient Egyptians were Neolithic farmers who ate bread, sweets and drank beer.

Gluten damages the gut of 83% of people. If they ask for proof of that, direct them to this:

http://gut.bmj.com/content/56/6/889.extract