The phrase "make mention of" means to refer to or mention something or someone. Antonyms for this phrase include "avoid mentioning," "conceal," "ignore," "overlook," "omit," and "skip." When we use any of these antonyms, we are deliberately choosing not to mention something or someone. For instance, if we decide to ignore or overlook something, we choose not to acknowledge it or give it attention. Similarly, when we omit or skip mentioning something, we choose to leave it out of a conversation or discussion. Hence, the choice of antonyms for "make mention of" depends on the speaker's intentions and the context of the conversation or discussion.