Why are catalyst not considered to be reactant or products even though they take part in chemical reactions?

A catalyst is a substance that speeds up the rate of a chemical reaction but is not consumed during the course of the reaction. A catalyst will appear in the steps of a reaction mechanism, but it will not appear in the overall chemical reaction (as it is not a reactant or product). Generally, catalysts alter the mechanism of the reaction in a substantial way such that the new barriers along the reaction coordinate are significantly lower. By lowering the activation energy, the rate constant is greatly increased (at the same temperature) relative to the uncatalyzed reaction.

when it is at an intermediate population density