I think this is one of those "1 question, 40 answers" questions.
My Lacey girl used to try this one (still thinks about it if she gets really overstimulated - it all basically stems from how weirdly her previous owners treated her, she actually ended up rearing up+over with one of them while doing this "trick") and if I tried circling or pushing her on with just my legs, she'd start side-stepping or continue backing up and the end result was some major rearing. Shed just rear and rear until I got off or stopped asking her to do whatever I was asking her to do.
There were/are two things that work with her:
a crop - it turned out that at her previous home, no one had apparently tried using a crop to solve this one! So that option was luckily not broken.
I got a short crop, made a little clip for it (so I could attach it to the saddle and only "magically" have it when she was acting up), attached it to my saddle, and took her out on a trail ride. I acted the way I always did, except that as soon as I felt her start to balk, I put my reins in one hand+loosened them up in case she jumped forward, and smacked her a good hard one on the booty with the crop (if there had been any question of whether she was going to continue on, I wouldn't have smacked her but at that point any balking was leading to "fun" so I didn't give her any lee-way).
She lept forward and we kept on our way quite happily. I remember being so surprised at how relaxed she was, post-smack. Apparently she really didn't care about precisely not going forward, she just wanted to pull a trick on me! Arabs!
I might have had to smack her a couple more times after that but those times became rarer and rarer. I still generally carry a crop on my saddle, just in case, but it's very very rare that I ever even pick it up. Usually it's just a "cool" accessory (it's purple and sparkly, hahahah).
riding on a very narrow trail with 7+ horses behind us - this isn't an option for most people, but pretty much directly after I got her out of the habit of this backing up junk, I got the chance to work at a summer camp leading trail rides. Lacey was my lead horse so she was leading day in and day out. If she tried backing up: "cool story bro, that horse behind you doesn't like your butt in his face so he's going to bite you in the butt!"
The trails were so narrow that there was no turning around and that horse behind her was a really good motivator to keep forward motion.
After that summer of trail rides (2 years ago), I think she's tried the backing up thing maybe twice and I was always ready with the crop. She hasn't tried it once in probably a year and a half. Same with the rearing; no more balking=no more rearing.
Good luck! I know how frustrating this little habit can be!!