The principle that explains why there must be the same number of atoms of each element on both sides of a chemical equation is the Law of Conservation of Mass.

Here's why:

* Chemical reactions involve rearranging atoms, not creating or destroying them. Atoms are the fundamental building blocks of matter. In a chemical reaction, atoms are simply rearranged to form new molecules.

* Mass is a fundamental property of matter. Since atoms are not created or destroyed in a chemical reaction, the total mass of the reactants (starting materials) must equal the total mass of the products (substances formed).

* To ensure the mass is conserved, the number of atoms of each element must be the same on both sides of the equation. This is achieved by balancing the chemical equation.

Therefore, the Law of Conservation of Mass dictates that a balanced chemical equation reflects the fact that atoms are neither created nor destroyed in a chemical reaction.