The antonyms for the phrase "buddy up" include "avoid," "separate," "isolate," "avoid association," or "disengage." These words imply a lack of desire to forge a close bond with someone or deliberately distance oneself from others. When we fail to buddy up with someone, we miss out on a chance to connect and form deep relationships that come with benefits such as increased social support and shared experiences. On the other hand, there can be times when it is necessary to avoid or separate from others, especially in situations where we need to focus on individual tasks or maintain our own personal space.