> This is a subject of irrationality I have trouble understanding

That's because you are utterly, terribly wrong, and like you millions of people, including doctors. And that's why so many people have trouble losing weight. You think you have THE TRUTH, your truth is not working, then blame the world.

Just two things:

1) The actual first law of thermodynamics is:

(Calories In) - (Calories Out) - (Calories Stored) = 0

Note in particular this is a constraint, i.e., the absence of causality assumptions.

2) You don't eat pure energy. After the first law there is the second: http://www.nutritionj.com/content/3/1/9

3) Please read Taubes.