When balancing a chemical equation, why must the formula subscripts remain unchanged?

The formula subscripts can't be changes since the subscripts tell you the characteristics of the molecules being talked about
for example H₂+1/2O₂⇒H₂O is not the same thing as H₂+O₂⇒H₂O₂  even though the only thing that changed is the added oxygen to water.  they show completely different reactions since water and hydrogen peroxide are different chemicals.  As you can see with the coefficients, they are are even balanced differently.

I hope this helps you if you have any further questions feel free to leave them in the comments.