Q: Why is mehr necessary on a woman that cheated on her husband? …… (text)
A: The cheating took place after the nikah. At the time of nikah she was faithful. At the time of nikah the male (husband) also promised to pay with faithfulness. Thus, even if she was unfaithful after the marriage had taken place, the husband cannot be unfaithful in his promise of giving the promised mehr amount. Two wrongs would not correct the situation as per case.
Allah Certainly Knows Best.