To deceitfully purport to remain on good terms with both sides in a conflict.

The proverbial saying ‘hold with the hare…’ is first found in John Heywood’s 1546 glossary A dialogue conteinyng the nomber in effect of all the prouerbes in the englishe tongue:

There is no mo [more] suche tytifils [scoundrels] in Englands grounde,
To holde with the hare, and run with the hounde.

When Heywood coined (or more probably, heard and then wrote down) ‘hold with the hare and run with the hounds’ hare coursing was a commonplace form of hunting for food. In more recent years it was undertaken for the entertainment of the onlookers. It is now illegal in the UK, although it still takes place. The ‘holding’ refers to the hare’s tactic of pressing itself low to the ground to avoid being seen, only bolting at the last moment.

The notion that one can’t legitimately support both sides of an argument is graphically illustrated by the hare/hounds imagery as there is no grey area – either the hare gets away or it is killed.

Heywood frequently attended the Tudor courts and it appears that the expression was well known there. Just a few years after Heywood it was repeated to Elizabeth I, albeit in the mirror image form. Bishop Richard Curteys included it in A sermon preached before the Queenes Majestie at Grenewiche, 1573:

They will say that white is blacke, and blacke white: they will runne with the hare, and holde with the hounde.