Antonyms for the word "show sympathy" include "disregard," "ignore," "neglect," "repudiate," and "spurn." These antonyms denote a lack of empathy or concern for someone's situation or feelings, and may be indicative of a callous or indifferent attitude. When we fail to show sympathy, we risk damaging our relationships with others or contributing to their feelings of isolation, loneliness, or despair. Therefore, it is important to cultivate a sense of empathy and compassion towards others, especially in difficult times, and to actively work against attitudes of indifference or apathy.