a stick to beat someone with
stick to beat (someone or something) with
Something, often a mishap or misdeed, that is used as an excuse for criticism. Even the slightest mistake by Stan was enough to give the boss a stick to beat him with.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
a stick to beat someone withor
a stick with which to beat someoneBRITISH
COMMON If someone uses something as a stick to beat someone with or a stick with which to beat someone, they use it to punish them or cause embarrassment or difficulty for them. Republicans had hoped to use foreign policy as a stick to beat the President with. Note: You can also say that someone uses any stick to beat someone, meaning that they take every opportunity they can to punish someone or cause embarrassment or difficulty for them. The Socialist opposition, of course, will use any stick to beat the government.
Collins COBUILD Idioms Dictionary, 3rd ed. © HarperCollins Publishers 2012