The phrase "flying pig" has become a popular idiom meaning something that is impossible or unlikely to happen. However, there are several synonyms that can be used in place of it. One such term is "pink elephant," which describes an imaginary creature that is also improbable. Another synonym for "flying pig" is "unicorn," which represents something rare or non-existent. "Pipe dream" is another idiom that can be used in place of "flying pig," meaning a hope or desire that is unlikely to come true. Lastly, "pie in the sky" is another possible replacement term. This phrase suggests a lofty or utopian idea that is unattainable in reality.