Antonyms for the phrase "climbs onto" could include "descends from," "exits from," or "steps off of." These words imply a downward motion or a leaving of a higher position. Other antonyms may be "descends down," "drops off," or "falls off," which imply a sudden loss of height or support. These phrases may be used to describe downward movements or in situations where one is leaving a higher place or position. While "climbs onto" implies a sense of progression and upward motion, antonyms such as these suggest a reversal of that movement.