Fat feeds into the Krebs cycle.
Look it up.
Look, the point is that when insulin rises, fatty acids get stored. If you keep insulin stable and low, then there is simply no reason to store fatty acids.
You should be able to tell that its not at all about calories or any notion of a negative/positive caloric balance. Our bodies dont work that simply.
The food we consume today has to be converted and synthesized amidst a long-term supply of food.
The reason a zero-carbohydrate diet works is because eating only fat and protein provides your body with the best opportunity to mobilize fatty acids and provides no reason to store fat by making triglycerides.