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I'm never sure why people think beating their horse with a rope is weirdly kinder than learning how to use a schooling whip properly (buy one with the big leather flappy end). (I am sure I saw a video advising slapping the 'giddy up rope' against waterproofs to make a noise to spook your horse forward - bad, bad idea! )
The advantage of a whip being that it doesn't affect the contact you have with the horse's mouth, and you are reinforcing and refining the leg aid. And from what you say, your issue is that he ducks behind the leg in the arena too, as an evasion. Try to sharpen him to the leg aids with lots of acute transitions (halt to trot, walk to canter), maybe lateral work.
Incidentally for rearing as an evasion, turn him in small circles bending his neck to one way (they can't go up with a bent neck).
But everything should be built on him going 'forwards' from the leg.
Who says I'm beating him with a rope?!
I'm literally flicking it up and across my shoulders to make a sound!
I won't carry a whip. End of. If a dog or a child wouldn't walk into a room or something would you really think that hitting them with a whip to reinforce your aid is kinder than making some kind of sound or something to push them on?! Smacking him escalates it. Using a sound doesn't
And aren't you saying to buy a whip with a flappy end so it makes a noise rather than stinging? So what's the difference?!