not give an inch
US /nɑt ɡɪv ən ɪntʃ/
UK /nɑt ɡɪv ən ɪntʃ/

1.
to refuse to change your opinion or decision, even when people try to persuade you
:
•
Despite strong opposition, the mayor would not give an inch on the new policy.
•
The negotiators would not give an inch, leading to a stalemate.