"At loggerheads" is an idiomatic expression that means to be in a state of intense disagreement or conflict with someone. Some synonyms for this phrase include being in a dispute, at odds, in conflict, in disagreement, in opposition, in a standoff, and at a stalemate. When two parties cannot resolve their differences and are fiercely opposed to one another, they are said to be at loggerheads. This phrase can be used to describe personal conflicts as well as political or business disputes. It is essential to find common ground and reach an agreement to avoid remaining at loggerheads indefinitely.