The amount of fat you need varies depending on your position of play. It may be acceptable for certain players like locks and props to carry slightly more body fat for protection. Fats and oils are important sources of fat-soluble vitamins (A, D, E, K) and "essential fatty acids" which are necessary for optimal health and performance.
Your eating plan has limited your intake of both "added" and "hidden" sources of fat. Butter, margarine, avocado pear, peanut butter and oil are examples of added fats, whereas hidden fats are those found in high fat cheeses, many processed meats (e.g. Viennas, polony, salami) and snack items (chocolates, crisps, nuts).