The phrase "making one's hair stand on end" refers to something that is frightening, startling, or spooky. This is an idiom that is often used to describe a hair-raising experience that causes fear or anxiety. The antonyms or opposite words for this phrase could include relaxing, comforting, soothing, or reassuring. These are the words that can be used to describe experiences that calm and ease the mind, rather than making one's hair stand on end. Examples of such experiences include a warm cup of tea, listening to calming music, or taking a gentle stroll in nature.