Antonyms for the phrase "showing sympathy" are words that express a lack of concern or understanding for someone's feelings. For instance, "insensitive," "unsympathetic," and "unfeeling" are some of the antonyms that come to mind. Each of these terms conveys a sense of detachment or aloofness towards the person's plight, indicating that the person showing these characteristics doesn't care about the other person's suffering or isn't capable of understanding it. Conversely, antonyms such as "cold," "callous," or "heartless" suggest an active disregard for the other person's emotional state, emphasizing the harm that such attitudes can cause. Regardless of the antonym, it's important to remember that showing sympathy is an essential human trait that helps build empathy, understanding, and mutual support.