Agree to check physical issues thoroughly first. Even though he’s doing fine on the flat it sounds like, there can be pain triggers in the hind end or back that are fired during the different mechanics of jumping.
If all checks out, work closely with your trainer (and don’t be afraid to ask for multiple sets of eyes either). Both of my horses are very sane & sensible, but if I make the mistake of catching them in the mouth or hanging on their face approaching, during, or leaving a jump, they will start rushing & jumping flat. It’s very common when a horse is anticipating something uncomfortable.
And you’re certainly not alone, not very many of us are Michael Jung! I do a lot of schooling on my own (have often used video camera on tripod so I can review afterwards), and have several methods that help a lot when I (or horse) need reminders:
-Put on neck strap (aka my old stirrup leather or the tie-down I found in a trash pile, LOL, or use mane) & make a rule that I must keep my hands on it from 3 strides out to 3 strides after the jump. My amazing jump trainer who has jumped around Burghley very rightly says, “The only thing you can do that close to the jump is mess it up.”
-Halting before or after often just pisses mine off too. We must “prove” to them that we’re not going to inadvertently punish them over the jump. This can require a big leap of letting go & if you’re not comfortable, have your trainer do it first. I make a teensy thing & will just take them over it repeatedly on a completely loose, swinging rein. Almost on the buckle. Working it on a circle or figure 8.
Obviously, you must put safety measures in place depending on your horse. This may require an enclosed space. But when he’s blowing through my half-halts & just getting more balled up, this has been the #1 answer, gifted to me by both Wofford & Becky Holder, because holding on more is not going to help. And though our brains try to convince us otherwise, we’ll never be able to out-muscle 1400 lbs of equine. You let the jump do the work.
Yep, he usually blows through it the first time, might even knock the pole down. But I MAKE myself keep the reins long, zero contact, I just sit up, get off his back, stay balanced & let it happen. I even talk or hum out loud, keeping all the energy easy & light. After time or two (or more, with my older one who was much more stubborn), he goes, “Oh, this is not a big deal, I can chill.” And I repeat until it is so uneventful he’s about to yawn.
I can do it with a single jump now, but when he was greener, I would use more placing/trot poles, to keep brain & feet busy & honest.
But this renews our trust contract of “this only has to be as hard as you want to make it, horse.”
Again, lots of caveats depending on horse, rider comfort level, etc. But I’ll stop the missive, you get the idea.