Why does an oxidizing agent undergoe reduction?
Because of the way we define
A species that undergoes
Given these ideas and conceptions, an oxidizing agent is conceived to ACCEPT electrons from the species that is oxidized. And if it accepts such electrons it is necessarily reduced.
Consider the oxidation of coal:
Both reactants, are zerovalent, and are presumed to have neither accepted nor donated electrons. The carbon dioxide is the product of the redox reaction where the reducing reactant, carbon, has donated 4 electrons to the oxidizing oxygen, which clearly has been reduced in the product. To put oxidation number labels on products and reactants, we have:
Clearly, carbon has been oxidized. Why clearly?
But for every electron loss, for every oxidation, there is a corresponding electron gain, a corresponding reduction. And here, clearly, the oxygen has been reduced. Capisce?