The correct answer is option 2: Liver. The liver plays a crucial role in breaking down fats to produce cholesterol. Cholesterol is a type of lipid that is essential for various physiological functions in the body, including the production of hormones, digestion of fats, and the formation of cell membranes.

The liver acts as a central processing unit for cholesterol metabolism. It synthesizes cholesterol from various sources, including dietary intake and the breakdown of fats in the body. Once formed, cholesterol is either stored in the liver or released into the bloodstream for distribution to other tissues.

While the intestine also plays a role in the absorption of dietary cholesterol, it does not break down fats to produce cholesterol. The lungs primarily function in the exchange of gases and do not have a direct involvement in cholesterol metabolism. Similarly, the kidneys are responsible for filtering waste products from the blood but do not actively break down fats to produce cholesterol.

Therefore, the liver is the organ primarily responsible for breaking down fats to produce cholesterol in the body.