If our body fat is made up almost entirely of the fats we eat, why don't we just drastically REDUCE FATS in our diet?

A low-fat high-carbohydrate diet can decrease your ability to lose weight, particularly body fat. The issue with this type of diet is that when most people go on a low-fat diet, typically they don't consume healthy high fiber, unrefined carbohydrates. Most people will replace high fat foods with foods that are high in refined, processed carbohydrates. When replacing fat with carbs, you also get a surge in blood glucose which leads to a spike in insulin levels. Elevated insulin levels inhibit the activity of the enzyme hormone-sensitive lipase.
This enzyme is responsible for breaking down stored fat (triglycerides) into glycerol and fatty acids; the latter which will be used as a source of energy. The ideal way to follow a low-fat high carb diet is to make sure you still consume adequate amounts of healthy fats such as those found in olive oil, nuts like almonds and cashews as well as fish such as sardines and salmon. Small portions are key. Include small portions of high-fiber whole grains along with a source of protein i.e. brown rice w/grilled chicken. By consuming high-fiber whole grains with protein, it will take a longer time to digest the meal and absorb the glucose from the breakdown of the carbohydrates. This way, you avoid the surge in blood sugar and insulin that's common after consuming a meal rich in refined, low-fiber carbohydrates.
Another tip-to lose body fat do cardio exercise on an empty stomach in the AM and strength training later in the day; at least a couple of hours after a meal as you'll need the energy for your workout.

More you will find out here....