Here's a breakdown of the meaning:
* Loggerheads: Originally referred to a type of large hammer used by shipwrights. The image is of two people bashing their heads together, unable to reach an agreement.
* At: This preposition implies a state of being in a specific situation.
* Loggerheads: The core of the idiom, indicating the stubborn and uncompromising nature of the conflict.
Examples:
* "The two countries have been at loggerheads over trade agreements for months."
* "The neighbors are at loggerheads over the boundary line."
* "The boss and the employees are at loggerheads about the new work schedule."
Synonyms:
* At odds
* In a standoff
* In a deadlock
* At a stalemate
* In a dispute
* In a disagreement
Note: The idiom "at loggerheads" is always used in the plural, even when referring to two individuals.