No, I do not believe in punishing the horse for refusing the jump or running out on a jump - there is always a reason for a horse to do that and I believe the majority of the time it falls into two categories:
1. Lack of confidence/experience on the horses part
2. Incorrect riding on the rider's part
Denny Emerson brought up a rather nervous horse, Rosie, who lacked confidence in the beginning (now she is jumping advanced, I believe). This is a post from him about this horse, that you can find on his FB page (rather a collection of many posts about her):
"The way that we got Rosie to stop refusing and to start jumping was, 1. to get her used to the idea that she was NEVER going to be punished for not going---
And, 2. that she wasn't going to get "lied to" about the take off spot.
And, 3. that she would not be held or tightly constrained on her way to the jump.
And, 4. that it was going to be casual, no big deal----"
"This mare used to quit at jumps one foot high. So we just fiddled around, tried to make her calm, and NEVER punished her when she would stop.
Jack LeGoff used to say,
"Boldness comes from confidence. Confidence comes from success. So it is the job of the trainer to create lots of situations which guarantee success."
We did that, and Rosie gradually lost her fear of jumping.
It seems so simple, Jack's little "mantra" but many riders and trainers still use force. Which is maybe why Jack won all those gold medals, and the others do not."
Here is a video of Denny riding Rosie when she was only 4, and just starting over fences:
And then a perspective from Shelby Dennis, who holds the same views as myself and Denny about punishing before fences, specifically her blog post "The Myth of a Bad Horse", linked here: https://www.milestonequestrian.com/blog
Here are is a story pulled from her blog post:
"Let me tell you a story that really opened my eyes with regards to these cases of “bad” horses. Recently, I took in a client horse who had a history of competing in eventing and doing quite well. The horse was successful over fences, never stopped and was forward to fences. Overall, he was always a lazier horse who required lots of leg to ride and didn’t have an aptitude to go forward much. Randomly, he started sucking back more and more under saddle. He would also start resisting lateral work like leg yields, crow hopping or tripping instead. He became more and more dead to leg and the solution suggested to his owner by a trainer was to use a crop or spurs to urge him forward. Not an odd request, a very common one seen in most training barns, in fact. Also, not inherently problematic, but let me tell you why it sometimes can be and why it’s so common for people to make this mistake.
So, this horse would express disobedience or “disrespect” by backing off, trying to move down to slower gaits or jogging around like a western pleasure horse. He would get a smack with crop, asked to go forward, and pressure was removed when he did. Oddly he just kept backing off. More pressure, more smacking, “send him forward”," “make him go”. He would resist sometimes by hopping up to rear, but then going. The owner was doing what they were told by a trainer, a professional they trusted and at the time, they trusted the method to work for the horse. For a while, it worked just enough and they even did a basic veterinary exam, got him some maintenance of joint injections which seemed to help for a short time, even though he still remained lazy and in need of motivation to go forward. Then his behavioural issues increased. Walking away from the mounting block, then rearing when riders would mount. Evading the bit, hollowing out his back, refusing to go forward even when the pressure of a whip or spur was added, slamming on the brakes randomly under saddle and rearing. The owner did everything that many would suggest like checking saddle fit, chiropractor and massage. They even went above and beyond to check for kissing spine, to no avail. After further therapy to rule out any back pain, the horse was put back into work and was a bit better about not evading the bit, still not forward. The owner was still having to heavily use a whip to send him forward and smack him hard right behind their leg to “reinforce” their aids. Again, a very highly suggested and commonly used method by many many trainers and suggested to this person by their trainer.
The use of the whip to force him forward worked for a short while again, so his work load was increased as he got back into fitness on the flat, still requiring fairly heavy use of the whip. He started back over fences and was better behaved over fences than he typically was on the flat. The owner then went away and had a friend getting on him. The horse started to squeal and rear very high up when the friend first got on, but since this was after him having a short time off, it didn’t raise any major alarm bells. Friend was a good rider so rode him through it and was fine. Owner came back, could not get the horse forward under saddle and he would start to resist the heavy whip use and still lose forward motion. He would bolt away from the mounting block before getting on. The owner sought help out from another trainer, who proclaimed the horse as a “dominant” type and proceeded to try to enforce further dominance over him, getting fairly aggressive in their quest to have him relax at the mounting block. Owner admitted to being quite uncomfortable, but was not a professional so let the professionals do their job despite said discomfort. The horse then started to strike out or kick at people even during ground work, resorting to biting and acting out. The suggestion by many was predominantly that the horse was just ill-behaved and needed to learn some manners and be put in his place…."
Here is a video of her and her horse Milo's transformation, who would very often refuse fences: