log ‧ ger ‧ heads /ˈlɒɡəhedz $ ˈlɒːɡər-, ˈlɑː-/ BrE AmE noun
[ Date: 1800-1900 ; Origin: loggerhead 'stupid person, large head, type of heavy tool' (16-20 centuries) , from logger 'block of wood' (16-18 centuries) (probably from ⇨ ↑ log 1 ) + head ]
be at loggerheads (with somebody) if two people are at loggerheads, they disagree very strongly
be at loggerheads (with somebody) over
He is at loggerheads with many of his own party over the issue of taxation.