The phrase "favorable mention" often implies a positive remark or endorsement. Its antonyms, such as criticism, disapproval, or censure, suggest negative evaluation or condemnation. Instead of a glowing reference, unfavorable mention might mean a detracting or harmful comment about a person, product, or idea. Other antonyms to favorable mention could be disregard, neglect, or indifference, indicating a lack of attention or recognition rather than a positive or negative judgment. Depending on the context, synonyms or antonyms to favorable mention can have different connotations and shades of meaning, reflecting the speaker or writer's attitude, tone, and purpose.