If two or more people or groups are at loggerheads, they disagree very strongly with each other. For months dentists and the health department have been at loggerheads over fees France was left isolated and at loggerheads with other EU member countries over its refusal to fall into line with demands to cut state borrowing. be at loggerheads (with sb) if two people are at loggerheads, they disagree very strongly be at loggerheads (with somebody) over (loggerhead (16-20 centuries), from logger (16-18 centuries) (probably from LOG) + head)
We were really at loggerheads about what to do with the money we found on the side of the road; she said we should turn it in, I said we should set it free.
A very large marine turtle (Thalassochelys caretta, or caouana), common in the warmer parts of the Atlantic Ocean, from Brazil to Cape Cod; called also logger-headed turtle