I've seen this question come up a bunch of times, and it seems most people don't understand why this is taught to horses. Shaking your horse back has a practical purpose, it comes from Vaquero horsemanship which is the foundation of NH. It's essential for when you're doctoring cattle. Here's a picture where I'm working on a calf with my horse. I'm holding the calf down, you can see my horse has stepped up to give me slack in my lariat, the dark rope is my mecate lead that's part of my reins. I need the rope loose so I can get the loop end off the calf's head and put it on it's front feet. You don't want the rope on his neck more than you have to and when you're done you can let him loose and he'll simply kick the rope off. So once I have the front feet in the loop I shake my mecate rope and my horse will backup and retighten the lariat for me. That's where shaking them back comes from, I'm holding the calf so I can't get up and back my horse. Also if the rope gets a little loose and the cow tries to kick free that will shake the rope and my horse will step back and make it a little tighter.
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