What term refers to a damaging remark or criticism against someone?

The term that refers to a damaging remark or criticism against someone is "aspersion." This word specifically denotes a false or misleading charge meant to harm someone's reputation or character. When someone casts an aspersion, they are essentially making disparaging comments that can negatively affect how others perceive the individual in question. This reflects the idea of slander or defamation, as it implies a calculated intent to undermine the credibility or integrity of the person targeted.

In the context of the other terms, "augury" typically relates to omens or predictions, while "antithetical" means directly opposed or contrasted, often used to describe conflicting ideas. "Broach" refers to the act of introducing a topic for discussion, which does not connotate any form of criticism. Therefore, "aspersion" is the most fitting term for describing a damaging remark or criticism.