You encounter free radicals every day as you expose yourself to food, pollution, pesticides and chemical beauty products. These free radicals damage cells, potentially causing disease and accelerating aging. Olive oil is a natural source of the antioxidants vitamins E and A, which fight free radicals -- and the benefits are there regardless of whether the oil is ingested or rubbed into the skin in the form of soap. Olive oil also contains oleocanthal, a compound touted for its anti-inflammatory benefits. Inflammation in the body can compromise your immune system and put you at risk for illness and disease, including chronic skin rashes, heart disease and digestive problems.