These works seem to disagree with you.

Your turn. Please do try to disprove the law of conservation of energy.

Swinburn B, Sacks G, Ravussin E. Increased food energy supply is more than sufficient to explain the US epidemic of obesity . Am J Clin Nutr. (2009)

Lack of evidence for high fructose corn syrup as the cause of the obesity epidemic
Leibel RL, et al. Energy intake required to maintain body weight is not affected by wide variation in diet composition . Am J Clin Nutr. (1992)

Golay A, et al. Similar weight loss with low- or high-carbohydrate diets . Am J Clin Nutr. (1996)

Golay A, et al. Weight-loss with low or high carbohydrate diet . Int J Obes Relat Metab Disord. (1996)

Luscombe-Marsh ND, et al. Carbohydrate-restricted diets high in either monounsaturated fat or protein are equally effective at promoting fat loss and improving blood lipids . Am J Clin Nutr. (2005)

Bray GA, et al. Effect of dietary protein content on weight gain, energy expenditure, and body composition during overeating: a randomized controlled trial . JAMA. (2012)

Noakes M, et al. Effect of an energy-restricted, high-protein, low-fat diet relative to a conventional high-carbohydrate, low-fat diet on weight loss, body composition, nutritional status, and markers of cardiovascular health in obese women . Am J Clin Nutr. (2005)

Keogh JB, et al. Long-term weight maintenance and cardiovascular risk factors are not different following weight loss on carbohydrate-restricted diets high in either monounsaturated fat or protein in obese hyperinsulinaemic men and women . Br J Nutr. (2007)

Farnsworth E, et al. Effect of a high-protein, energy-restricted diet on body composition, glycemic control, and lipid concentrations in overweight and obese hyperinsulinemic men and women . Am J Clin Nutr. (2003)

Brinkworth GD, et al. Long-term effects of a high-protein, low-carbohydrate diet on weight control and cardiovascular risk markers in obese hyperinsulinemic subjects . Int J Obes Relat Metab Disord. (2004)

McLaughlin T, et al. Effects of moderate variations in macronutrient composition on weight loss and reduction in cardiovascular disease risk in obese, insulin-resistant adults . Am J Clin Nutr. (2006)

Sargrad KR, et al. Effect of high protein vs high carbohydrate intake on insulin sensitivity, body weight, hemoglobin A1c, and blood pressure in patients with type 2 diabetes mellitus . J Am Diet Assoc. (2005)

Boden G, et al. Effect of a low-carbohydrate diet on appetite, blood glucose levels, and insulin resistance in obese patients with type 2 diabetes . Ann Intern Med. (2005)

Heilbronn LK, Noakes M, Clifton PM. Effect of energy restriction, weight loss, and diet composition on plasma lipids and glucose in patients with type 2 diabetes . Diabetes Care. (1999)

Parker B, et al. Effect of a high-protein, high-monounsaturated fat weight loss diet on glycemic control and lipid levels in type 2 diabetes . Diabetes Care. (2002)

Thomson RL, et al. The effect of a hypocaloric diet with and without exercise training on body composition, cardiometabolic risk profile, and reproductive function in overweight and obese women with polycystic ovary syndrome . J Clin Endocrinol Metab. (2008)

Strasser B, Spreitzer A, Haber P. Fat loss depends on energy deficit only, independently of the method for weight loss . Ann Nutr Metab. (2007)

Astrup A, Meinert Larsen T, Harper A. Atkins and other low-carbohydrate diets: hoax or an effective tool for weight loss . Lancet. (2004)

Golay A, et al. Similar weight loss with low-energy food combining or balanced diets . Int J Obes Relat Metab Disord. (2000)