back out vs pull in one's horns

back out and pull in one's horns both are verbs.

Word	Noun	Adjective	Verb	Adverb
back out	No	No	Yes	No
pull in one's horns	No	No	Yes	No

As verbs, back out and pull in one's horns are synonyms defined as:

back out and pull in one's horns: make a retreat from an earlier commitment or activity

Other synonyms of back out include back away, crawfish, crawfish out, pull back, retreat, withdraw.

back out (verb)	pull in one's horns (verb)
make a retreat from an earlier commitment or activity	make a retreat from an earlier commitment or activity
move out of a space backwards