Fat has gotten a "bad rap" in years past. As one of three major macro-nutrients in food [the other 2 being carbohydrate & protein], the universe intended for us to eat fat! Somehow in recent years, we've taken the glorious gift of "fat" and tried to eliminate it from our diets. The thought process seemed to make sense, if we eliminate fat from our diet, we will be skinnier and healthier - it must be the fat in our diet making Americans fat, contributing to the obesity epidemic. Yet the "low fat" fad didn't get us any better results. In fact, the low fat fad created fatter Americans.
In the last 20 years, fat consumption has decreased 11% in this country. What has been the result of 20 years of following a diet low in fat and high in carbohydrates? It has made Americans the most obese people on this planet. In fact, during the last 20 years, while fat intake has decreased, obesity has increased 32%! 
Let's keep it simple. We can't single out 1 of the 3 macro-nutrients and say it's the problem. It's not fat in itself that's bad for you, but certain types, particularly trans fats that are linked with disease. The main types of fats include: monounsaturated, polyunsaturated, saturated, and trans fats [called partially hydrogenated fats].
Trans fats [partially hydrogenated fats] are created in a laboratory by adding hydrogen gas to a liquid vegetable oil, to create a solid oil at room temperature. The goal? To create a longer shelf life for products. If natural animal fat was used, the product would go rancid within days. Which is why when you make homemade cookies they don't last forever like "Chips Ahoy" which contain partially hydrogenated soybean oil. So what's the problem with these trans fats? In adding the hydrogen, hydrogenation, rearranges the fat into an unnatural form that doesn't agree with our body.
Fat is actually an essential part of our diet for 2 main reasons: it forms the lining of the each and every cell in our body and it helps our bodies form hormone-like compounds called eicosanoids [which help regulate blood pressure, heart rate, and the nervous system]. Also, fat carries fat soluble vitamins [A, D, E & K], so inadequate fat intake can lead to vitamin deficiencies vitamins.
"Fat also helps maintain healthy hair and skin, protects vital organs, keeps your body insulated, and provides a sense of fullness after meals." 
So don't eliminate fat from your child's diet; just eliminate trans fats. The other fats [monounsaturated, polyunsaturated, and saturated fats] are necessary nutrients in everyone's diet [even those who are overweight]. It's all about moderation - too much of any macro-nutrient means too many calories. Consuming more than you burn means weight gain. So enjoy plenty of healthy fats [olive oil, nuts, avocados, flax seeds, and cold-water fish like salmon], and also enjoy saturated fats in moderation [red meat, poultry, butter, whole milk, and coconut oil]. What we all need to work on is eating more vegetables and other plant foods (fruit, nuts, seeds, legumes) that provide us with disease fighting phytonutrients. So be sure to eat more veggies (couldn't resist mentioning that!).
Susan McCreadie, MD is a Holistic Pediatrician and co-founder of get REAL for kids™. She shows parents how to find REAL health for their child, so they can stop treating their child's symptoms and instead find solutions that help their child heal from the inside out.
1. Guide to Healthy Eating by David Brownstein, M.D. & Sheryl Shenefelt, C.N.