How would an unbalanced chemical equation convey misleading information about what took place during a chemical reaction?

Balanced means you can do proper calculation - each element has to be balanced on left and right - thus matter is conserved as well. Make sure that chemical equations are balanced because it will lead to the right calculations of the amounts (of the substances) involved in the reaction. It is important that you do not change the identities of the substances involved so that you can count properly the number of atoms of an element in the reaction.