First, a bit of information about fat.
Dietary fat and body fat are two different things. Dietary fat (what you eat) is converted to fatty acids and absorbed in the small intestine then transported to the liver before circulated in blood and these fatty acids are oxidised for ATP production (energy). Similarly, body fat (body stores) is liberated and converted to fatty acids in the liver before being used for ATP. Thus, our body has infinite stores of energy and requires fat to live.