The phrase "fall all over" typically means to show excessive affection or love towards someone. The antonyms for this term would be to be indifferent, cold, or distant towards someone. Other antonyms may include being reserved, aloof, disinterested, or even hostile towards someone. These terms are often used to describe a lack of affection or a lack of interest in somebody. The opposite of falling all over someone would be to approach a situation with a level-headed and objective approach, rather than letting one's emotions take over. It is important to recognize and understand the value of balance, rather than always being either too affectionate or too distant.