1.
like cats and dogs; on very bad terms; bitter rivals
An idiomatic expression describing two people or groups who are always fighting or who cannot get along at all. Literally means "the relationship of dogs and monkeys," as dogs and monkeys are traditionally believed to be natural enemies in Japanese culture.
We're on terrible terms with the neighboring department and always clash in meetings.
One of the most well-known Japanese idioms. The expression comes from the folk belief that dogs (犬) and monkeys (猿) are natural enemies. Note that Japanese uses "dogs and monkeys" where English uses "cats and dogs." Usually ～と～は犬猿の仲だ, or 犬猿の仲の + noun. Related: 水と油 (oil and water — also describes incompatibility), 仲が悪い (on bad terms — straightforward expression).