In most organic compounds the halogen atom is bonded covalently to carbon and is therefore not available as a free halide ion in solution. Silver nitrate detects halogens by precipitating insoluble silver halides, but this requires the halogen to be present as ionic chloride, bromide, or iodide. Direct addition of silver nitrate to the organic compound fails because covalently bound halogen does not ionise and cannot form the precipitate. Sodium fusion solves this by reacting the compound with sodium metal, converting the covalent halogen into sodium halide (NaX), which is ionic and water soluble. The aqueous sodium fusion extract is then acidified with dilute nitric acid (to destroy cyanide or sulphide that would otherwise interfere) and treated with silver nitrate to give the characteristic precipitate. The claim about silver nitrate not dissolving in organic solvents misses the real point about covalent bonding. Raising temperature alone does not free the halide ion. Halogens do not simply evaporate away. This conversion of covalent halogen to ionic halide is the NCERT rationale. Plausibility check: only ionic halide can precipitate with silver ions, so fusion is essential.