From Longman Dictionary of Contemporary Englishnot give/budge an inchnot give/budge an inchREFUSEto refuse to change your decision or opinion, even though people are trying to persuade you to do this Neither side is prepared to give an inch in the negotiations. → inch
Examples from the Corpus
not give/budge an inch• And even with his size he didn't know what to do with Braden standing over him and not giving an inch.• I was just a novice and he was fairly frightening, not giving an inch until he had sounded you out.• Once on the ground again she tried pulling the horse, but still it would not budge an inch. 