pull out vs back down

pull out and back down both are verbs.

Word	Noun	Adjective	Verb	Adverb
pull out	No	No	Yes	No
back down	No	No	Yes	No

As verbs, pull out and back down are synonyms defined as:

Other synonyms of pull out include back off, bow out, chicken out.

pull out (verb)	back down (verb)
remove, usually with some force or effort; also used in an abstract sense	move backwards from a certain position
move out or away	remove oneself from an obligation
bring, take, or pull out of a container or from under a cover
remove oneself from an obligation