Peanuts are legumes, and as such, you’re probably better off avoiding them, and that includes peanut butter. Legumes are generally not considered to be Paleo-friendly for a few reasons.
To start with, they have a high phytic acid content: an antinutrient that binds to nutrients in the seed and prevents the body from absorbing them. This can lead to digestive issues in some people, as well as mineral deficiencies.
Peanuts (along with some other non-Paleo foods, such as grains) are susceptible to a particular type of mycotoxins called aflatoxins. This type of mold has been linked to cancer when consumed in large doses. The FDA limits the percentage of aflatoxins a batch of peanuts can contain before it gets processed and sold, but the chronic effects of consuming small amounts of the mold every day have not been studied.
Polyunsaturated Fats (PUFAS)
Legumes are also high in a certain polyunsaturated fat called Omega-6. This particular type of fat is inflammatory, and we need to make sure we consume enough Omega-3s to counteract its effects. Because legumes, such as peanuts, are high in Omega-6s and devoid of Omega-3s, they are best avoided.
Caitlin Weeks has a comprehensive list of reasons to avoid peanut butter and go for the almond butter instead.