Why is it incorrect to balance a chemical equation by changing the subscripts?

The number of subscripts for each element in a chemical formula is like a form of spelling. Each chemical formula has its own unique set of elements and subscripts. For example, #"H"_2"O"# is the formula for water, and #"H"_2"O"_2# is the formula for hydrogen peroxide, a very different substance from water. For another example, #"CO"_2# is the formula for carbon dioxide, and #"CO"# is the formula for carbon monoxide, also a very different substance from carbon dioxide. So, if you change the subscripts in the chemical formulas in a chemical equation, you are actually changing the substances themselves.

Instead, you balance a chemical equation by changing the AMOUNT of each substance as necessary by placing a coefficient in front of the chemical formulas as necessary. If no coefficient is necessary, it is understood to be 1. The coefficient is multiplied times the subscripts for each element in the formula in order to determine the total number of atoms of each element on both sides of the equation.

So if I write the coefficient 2 in front of the formula for water, #"H"_2"O"#, so that it looks like #"2""H"_2"O"#, then I multiply the coefficient of 2 times the subscript 2 for hydrogen, and the subscript 1 for oxygen (No subscript is understood to be 1.).This gives me 4 atoms of hydrogen and 2 atoms of oxygen.