Why must chemical equations be balanced?
When we write a chemical equation we attempt to model, to represent an actual chemical reaction by chemical and mathematical symbols. For every chemical reaction EVER performed, the mass of the products is found to be EQUAL to the mass of the reactants from ALL sources. In other words, MASS is conserved. IF there are 10 g of reactants, there are necessarily 10 g of products.
This is why chemists (and teachers) INSIST that chemical equations are balanced. For every reactant particle, there must be a corresponding product particle. Garbage out MUST equal garbage in.