He neglects the metabolism one needs to maintain that fat tissue each and every day. One rough rule of thumb is 11/cal/day/pound to maintain your weight. Being 40 lbs overweight thus takes not just his (apparently trivial) 20 calories per day to gain that weight, but 440 additional calories per day to maintain it. If the weight was truly gained in a linear fashion, that's an average of 220 calories per day to maintain it, above the 20 per day to gain it. This is the real math. This is why weight gain and weight loss correspond to gross caloric intake and expenditure. The dynamic equilibrium of an organism's weight is a feedback mechanism in which the mass of the organism appears as the magnitude of the gain on the negative feedback term.
Someone who is truly obese, say someone who is 300 lbs who should 180 lbs, for example, is running an ongoing daily calorie surplus of 1320 calories through diet and lifestyle, not the 60 per day that Taubes would suggest. This is not an insignificant disparity, and this guy's work will be truly harmful wherever it is--help us all--taken seriously.
I could maybe take the rest of his ideas more seriously if he were not so obviously wrong right out of the gate.