The word 'exterminate' means to completely destroy or eliminate. Some antonyms for 'exterminate' could include phrases such as 'keep alive', 'preserve', 'protect', 'spare', and 'save'. These words all suggest the opposite of exterminating - to maintain, safeguard, or cherish. Other antonyms for 'exterminate' could include phrases such as 'tolerate', 'forgive', 'mercy', and 'compassion'. These words suggest a kinder, more merciful approach to eliminating pests or problems, rather than simply killing or destroying them. Overall, the antonyms for 'exterminate' suggest a range of alternative approaches to dealing with unwanted pests, problems, or challenges.