If you go into a caloric deficit your body will give a hormonal response. This response determines if your body will start using your fat reserves, your muscles or will just shut down. This hormonal response is dependent not only on how much you eat, but also on what you eat.
Eating a diet low in carbs enables your body to use up stored fat more easily and will leave you less hungry then a low fat diet. This makes it MUCH easier to stick to your diet.
"Fats make you fat" is a flat-out lie.
The effects of carbs - especially carbs with plenty of refined sugar - are the developed world's number one health care expense. They don't just cause obesity and diabetes, they also create inflammation which leads to heart conditions, strokes, and other life-changing disorders.
Unfortunately the food labelling industry has been promoting falsehoods for most of its existence. Labelling carbs more clearly, licensing sodas and diet sodas to limit access, and starting health programs to educate the population about carb abuse would do more to improve public health than anything else.