What term is used when someone attacks another's reputation?

Denigrate is the correct choice because it specifically refers to the act of belittling or insulting someone, particularly in a way that damages their reputation or standing. The term carries a connotation of unfair criticism or disparagement, suggesting that the attacker aims to tarnish the other person's image or credibility.

In contrast, the other terms do not convey the same meaning. To defend means to protect someone or something from attack or to uphold its value. Promote suggests supporting or advocating for someone or something, enhancing their reputation instead of attacking it. Support involves helping or providing assistance, which is contrary to the idea of damaging someone's reputation. Therefore, denigrate most accurately captures the action of attacking another's reputation.