[plural] [noun] - at loggerheads strongly disagreeingThe two families have been at loggerheads for years.The major cider makers are constantly at loggerheads with the farmers' union.Jones and White are at loggerheads over the way the issue was handled.
LOGGERHEADS
Meaning of LOGGERHEADS in English
Cambridge English vocab. Кембриджский английский словарь. 2012