Why must every redox reaction involve an oxidizing agent and a reducing agent?

An oxidizing agent oxidizes other element and itself gets reduced in a chemical reaction.

A reducing agent reduces other element and itself gets oxidized in a chemical reaction.

A redox reaction can be written as:

$\mathrm{A}+\mathrm{B}\to {\mathrm{A}}^{+}+{\mathrm{B}}^{-}$

Now the half reactions are:

$\mathrm{A}\to {\mathrm{A}}^{+}+{\mathrm{e}}^{-}$

$\mathrm{B}+{\mathrm{e}}^{-}\to {\mathrm{B}}^{-}$

Here, A is getting oxidized and its oxidation state changes from 0 to +1.

And, B is getting reduced and its oxidation state changes from 0 to -1.

Hence, B acts as an oxidizing agent. By accepting electrons, B gets reduced and oxidizes A. Electrons lost by A is gained by oxidizing agent B.

In a redox reaction, there is a transfer of electron between species.

Electron lost by a reducing agent is gained by an oxidizing agent.

An oxidizing agent oxidizes other element and itself gets reduced in a chemical reaction.

A reducing agent reduces other element and itself gets oxidized in a chemical reaction.

That’s why a redox reaction involves both the oxidizing and reducing agent.