The term "having recourse to" refers to the act of turning to someone or something for help, especially in difficult or challenging situations. The antonym for this phrase can be "self-reliant," which refers to a person's ability to handle problems and challenges on their own, without relying on external support. Alternatively, "avoiding" could be used as another antonym, which means to stay away from or keep clear of someone or something that may pose a threat or danger. Additionally, "ignoring" can serve as an antonym, indicating the lack of action or attention to solve a problem or address an issue.