Why must electrons cancel when oxidation and reduction half-reactions are combined?

When combining oxidation and reduction half-reactions to form a complete chemical reaction, the electrons must cancel because the overall process must be balanced and adhere to the principle of charge conservation.12

In any redox process, oxidation involves the loss of electrons, while reduction involves their gain. Because these reactions are analyzed as a complementary pair of electron-transfer processes, the total number of electrons released by the reducing agent must equal the number of electrons accepted by the oxidizing agent. If the electrons did not cancel, the resulting equation would not represent a possible, balanced chemical reaction, as it would imply a net gain or loss of charge within the system.132