It's not a question of belief. The first law of thermodynamics (energy in = energy out) cannot be violated. Even Gary Taubes and Dr. Michal Eades admit this. The point is that it doesn't give you the cause and effect relationship. Are people fat because they are lazy gluttons? The science says no. People eat too much/get lazy (slow metabolism) because of the hormonal effect of food. Insulin forces the sugar into fat cells (oversimplified, I know) - which leaves the cells hungry. Correct the hormonal problem (sugar/insulin) and the body has plenty of energy in the form of its own fat storage - and will burn this fat and not be as hungry.
Calories matter. You CAN eat paleo and not lose weight. Most people lose because they are less hungry and spontaneously reduce caloric intake. Its also okay to eat more one day and less the next. Skip meals once in a while or try IF.