I never want to be at loggerheads with my friends, but it occurs to me, as so often, I don’t know what I’m talking about.  So I found out:

‘At loggerheads’ is of UK origin. The singular ‘loggerhead’ occurs as a name in several contexts – as a species of turtle, a bird and as a place name. Originally, a loggerhead was none of these but was used with the meaning of ‘a stupid person – a blockhead’. Shakespeare used it that way in Love’s Labours Lost, 1588:
“Ah you whoreson logger-head, you were borne to doe me shame.”
A ‘logger-head’ was literally a ‘block-head’. A logger was a thick block of timber which was fastened to a horse’s leg to prevent it from running away. In the 17th century, a loggerhead was also recorded as ‘an iron instrument with a long handle used for melting pitch and for heating liquids.’ It is likely that the use of these tools as weapons was what was being referred to when rivals were first said to be ‘at loggerheads’.