When you want to express the idea of distancing or rejecting something or somebody, the term "push away" can be replaced by several synonyms. "Repel" suggests a forceful resistance, like two magnets that push each other away. "Shun" implies a social rejection, such as ignoring or avoiding someone intentionally. "Reject" conveys a more definite refusal, as in a job application or a romantic proposal. "Disown" implies a permanent severance of ties, usually referring to a family member or an inheritance. "Avoid" suggests a deliberate effort to keep a distance, like avoiding a particular topic or person. In any case, choosing the right synonym can help to convey your message more accurately and effectively.