The paleo idea is that we should eat what our ancestors ate before the invention of agriculture. It’s based on sound evolutionary reasoning and fair bit of empirical evidence.
The evolutionary argument is that we lived for millions of years on a paleolithic diet and only 10,000 years on an agriculture-based diet. Keep any evolving species in one specific environment for millions of years and it will optimize itself to survive in it. This means our body is optimized to survive in an environment that feeds it a paleolithic diet. It hasn’t had enough time to adapt to the modern diet.
The empirical evidence comes in several forms. First, the fossilized skeletons show that pre-agriculture humans had healthier skeletons than the post-agriculture ones.
The tall stature and strong bones of Paleolithic skeletons indicate that Paleolithic humans were in remarkably good health. Paleolithic humans were tall and slender; cavities and signs of malnutrition or stress in bones were rare; muscle attachments were strong, and there was an absence of skeletal evidence of infections or malignancy.
(From Perfect Health Diet.)
Then, there is stuff we know about animals. For example, elephants that are exposed to a diet resembling the paleolithic era—i.e., wild elephants—live longer than elephants exposed to a modern diet—i.e., zoo elephants. The rate of obesity among pet cats and dogs is much higher than that among wild wolves and tigers. One might be tempted to attribute this to the fact that wild animals are more likely to be malnourished because of the difficulty associated with obtaining food. However, feral rats that live in cities and eat food discarded by humans are obese too.