You almost never meet loggerheads by itself. People say two people, two groups, or two countries are at loggerheads, and it means they disagree very strongly — stuck, often angry, and not coming together. Newspapers still like the phrase; it is a little colourful and a little old-fashioned, but fully alive. It is not about heads, and it is not about cutting trees, even though logger and heads both sit in the spelling. For this meaning you do not walk around calling someone “a loggerhead” in ordinary modern talk; learn the whole chunk: at loggerheads (with someone).

針鋒相對、鬧翻（at loggerheads）