Oats are a type of grain, so if you’re still eating them, eliminating them from your diet should be the first step to living a Paleo lifestyle.
Gluten-Free ≠ Healthy
Oatmeal is technically gluten-free, but it is often cross-contaminated with other grains containing gluten, so unless it’s certified gluten-free, you may still be doing damage to your gut by eating oatmeal. Even if oatmeal is certified gluten-free, it contains another antinutrient that is similar to gluten and has been shown to cause digestive problems in some people. Some celiacs can handle oatmeal just fine, while some non-celiacs experience serious problems after eating oatmeal.
As with other grains, oats are high in various minerals, but because they also contain antinutrients, such as phytic acid, our bodies are largely unable to access those nutrients. Add to that the fact that oatmeal is extremely rich in carbohydrates (leading to a spike in blood sugar and insulin) and there’s just no good reason to eat it.
Mark Sisson even did a little self-experimenting to determine if oats could be included as part of a Primal lifestyle.