Etymology
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back down (v.)

in figurative sense of "withdraw a charge," 1859, American English, from notion of descending a ladder, etc. (the literal sense by 1849); from back (v.) + down (adv.).

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Definitions of back down

back down (v.)
move backwards from a certain position;
The bully had to back down
Synonyms: back up / back off
back down (v.)
remove oneself from an obligation;
Synonyms: chicken out / back off / pull out / bow out
From wordnet.princeton.edu