Why must chemical equations be balanced?
Because every chemical reaction that has ever been performed has conserved mass.
So you start with 10 g of reactant, from all sources. At most, you can get 10 g of product. In practice you are not even going to get that, because losses invariably occur on handling. Conservation of mass has been directly observed in every chemical reaction that has ever been performed (and certainly it will be observed in the experiments you do). The requirement to balance chemical equations stems from this balance, this stoichiometry.
See this old answer that expands on the concept of stoichiometry.
See here for another answer to virtually the same question.