The rationale behind the paleo diet oversimplifies both evolution and human history. For example, the idea that there was ever a single diet that every paleolithic person ate is completely false: human diets would have been based on geographically available foods, leading to not just a variation in what people ate but also differences in the evolution in nutritional needs.
Additionally, paleo followers outlaw grains and some plants based on the logic that paleolithic peoples would not have eaten these types of food before farming was invented 10,000 years ago, but archaeological evidence shows that humans consumed grains as early as 30,000 years ago and plants like tubers and water chestnuts fairly regularly.
In addition to its flawed logic, another problem with the paleo diet is that it can be too restrictive. Prohibiting dairy, beans, legumes, and grains can be difficult for people to maintain, not to mention flour and sugar; the former of these foods are rich in nutrients like fiber, calcium, and vitamin D as well, so it seems counterproductive to cut them out.
This diet may be good for short-term weight loss, but it can prove unsustainable in the long run.