Why should subscripts never be changed when balancing a chemical equation?

When balancing a chemical equation, you should never change the subscripts because doing so alters the chemical identity and composition of the substance itself rather than simply adjusting the quantity of molecules involved in the reaction.1

In chemistry, a subscript represents the specific number of atoms of an element present within a single molecule. For example, changing the subscript in $H_{2}O$ would result in a different chemical compound entirely. To balance an equation according to the law of conservation of mass, you must only adjust the coefficients—the numbers placed in front of a molecule—which indicate the total number of molecules participating in the reaction. By modifying only the coefficients, you ensure that the number of atoms of each element remains equal on both sides of the equation without changing the fundamental nature of the reactants or products.12