The antonyms for the phrase "give sign to" could include: hide, conceal, refrain, mute, or silence. When we give a sign, we are indicating something to others, whether it's a gesture, a signal, or a verbal cue. But when we choose not to give a sign, we are effectively avoiding any communication or indication of our thoughts, feelings or intentions. This can be intentional or unintentional, but either way it can create confusion or mistrust for those who are trying to read us. While giving a sign can promote clarity and understanding, sometimes keeping our thoughts or emotions to ourselves can be just as important.