고양이와 개사이 -- On cat and dog terms. Since cats and dogs are usually never on good terms, this expression could be used to describe two people who are habitually fighting, or at least treat each other like enemies. (고야이와 개는 언제나 새이가 좋지 못하니, 서로 원수처럼 지내는 사이를 이르는 말.)
