to completely refuse to change your opinion or decision
I’ve tried everything to persuade her but she won’t budge an inch.
Thesaurus: to not change, or to refuse to change your opinionsynonym
Main entry: inch
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not budge/give/move an ˈinch idiom
to refuse to change your position, decision, etc. even a little
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We tried to negotiate a lower price but they wouldn't budge an inch.
Useful english dictionary. 2012.