The word "refusing" implies a negative action or decision, but its antonyms convey different meanings. "Accepting" is the opposite of refusing, which denotes willingness, approval, or agreement. "Allowing" denotes permission, assent, or an affirmative decision. "Granting" implies that someone is giving recognition, approval, or a concession. "Consenting" implies agreement even if there may be reservations. "Approving" carries a positive connotation of possessing satisfaction or support. These varied antonyms suggest that there are many different ways to approach a situation, and sometimes it requires a diverse perspective to solve a problem.