We can see from these examples that phrasal verbs with back all have the feeling of changing our position or moving (backing) away from something.
back down (on/from something)
to take back a demand, an opinion, etc. that other people are strongly opposed to; to admit defeatShe refused to back down on a point of principle.
back out (of something)
to decide that you are no longer going to take part in something that has been agreedHe lost confidence and backed out of the deal at the last minute.
1 As the riot police approached, the crowd backed off.2 Back off! There’s no need to yell at me.
|A: “This project is already started, we can’t back out now!”
B: “You need to stop shouting! Back off and cool down, then we can discuss the problem.”