When balancing a chemical equation, why can you change coefficients, but not subscripts?

because changing subscripts would mean you are changing the basic composition of the substance.

Let's take a look at the simplest example:

##2H_2## + ##O_2## = ##2H_2O## (balanced equation)

The equation above means that in order to "create" 2 molecules of water (##H_2O##), you would need to mix 2 molecules of hydrogen gas (##H_2##) and 1 molecule of oxygen gas (##O_2##).

Now take a look at the illustration. This is what happens when you change the subscript in balancing equations instead of just putting coefficients.

As you can see, balancing the equation by changing the subscripts basically means that you are making a "new" substance rather than the one originally given in the equation.