The mass of substances produced in a chemical reaction is always equal to the mass of reacting substances. Therefore, you need to have the same number of each type of element on each side of a chemical equation. This is the whole purpose of balancing a chemical equation.
The purpose of coefficients in a chemical equation is that coefficients are used to show the ratio in which reactants combine and products for a chemical reaction.
A chemical equation must be balanced because the law of conservation of mass says that mass can neither be created or destroyed.