It's true. Backing cures biting. I've never met a horse that bites people and continues to bite after being taught to back up nicely.
Lipping, although less dramatic, is still considered biting and can be cured in the same way.
Nipping, although not technically biting, is considered to be annoying enough for some people that it warrants the same strategy. And again, the same strategy will work to cure it.
The reason it works is that horses use personal space bubbles as protection against each other. If one horse invades the others space without permission, they are driven out. Backing a horse simulates this same activity. Your goal is to literally drive the horse backward away from you. In that light however, if you back the horse up and fail to create space, in other words you stay at his head the whole time, its not as effective. You need to create space.
More importantly to remember then is... creating space cures biting. Try it out. Back your horse up next time she gets too mouthy, and notice how your horse stops lipping, nipping, or biting. Be assertive and match the energy output the horse is giving and then be kind and rewarding whenever you get the feeling your horse is a willing partner.
PS. If your horse bites others while you are riding, back up works here too. But if your horse bites you while riding. Consider getting a little extra help. I know exactly what to do and all it takes is a quick phone call to find out. Call 406-360-1390 and get a First time free coaching consultation with any horse related challenge you face. I want to hear from you.
God bless and stay safe