Eating fat doesn't raise blood glucose or insulin levels. Insulin is the hormone that stores body fat. Since dietary fat doesn't trigger the insulin response, it won't be stored as body fat. Unless you add carbohydrates to the mix.
Carbohydrates trigger the insulin response. When blood glucose levels are back to normal insulin in your bloodstream is still high. And insulin is busy storing glucose as body fat. When your glucose levels fall below normal, you get hungry. You eat more carbohydrates, and find yourself in the seemingly paradoxical position of being hungry and getting fatter at the same time.
To lose body fat, you must burn fat as fuel. This happens if you're not burning blood glucose instead. You can cut your body's glucose supply by eating low-calorie and low-fat, basically starving yourself. Or you can reduce carbohydrates, and increase your dietary fat intake, ultimately causing your body to burn stored fat.
"The latter approach has two advantages over the traditional calorie-controlled diet. First, you don’t have to go hungry. Second, by feeding your body on fats, your body will stop trying to find glucose and will naturally begin using its own stored fat."