Sigh.
This horse does not take the rein in question in EITHER direction, not just going to the right. Think about this. You don’t just correct this when it’s the outside rein, or when it’s the inside rein. You always have to be aware as to which rein the horse is not stepping in to.
It’s just that when its the outside rein, the rider thinks he is on it. So convenient, so misleading, so wrong. The problem is always the same, regardless of what direction you are going in, and you have to fix it even while riding in the other direction. You have to fix it all the time.
In the beginning, people have to learn ride the horse to step into the rein contact equally (and horses have to learn to step into the rein evenly). The idea of riding them very straight rather than jumping right into bending (and the equally baffling spiral seat theory, where the rider supposedly contorts her body into the shape of a pretzel, that is actually based on when the horse is IN COLLECTION and is up in front of you, and the very miniscule movements from the rider that bend it, NOT people in this situation) gets them thinking about both sides of the horse and what is going on underneath them.
Regarding what happens if your outside rein does not go forward when you bend the horse? His frame gets shorter and he curves into the outside rein, around your inside leg. You do not have to advance the outside rein for the horse to do this. The biggest evidence of this is to ride a spiral of decreasing size and see what happens if you advance your outside hand. The horses frame gets longer and longer and he CANNOT perform the smaller circle because he is now just too long and strung out to do it. He is following his nose around, rather than turning his shoulders. However, if you spiral in off your outside aids, the horses frame gets shorter and he is capable of staying on the smaller circle. In this way the horse becomes more gymnastic rather than more on the forehand.
It is hard enough to teach people to not drag their horses around on their inside rein; I cannot imagine telling them as beginners to put their outside rein forward, people as a rule can barely stand to hold onto it and keep it steady. The very first fix I usually have to work on a new student is to teach them to use their outside rein/aids effectively. Almost all of them are dragging their horse around on the inside rein while their outside hand floats forward and the horse lays on their outside leg. They protest, they have been taught the spiral seat! But the proof is in the horse, who is meandering around the arena. Horses that have not been taught to step equally into both reins first and then bent by curling around the inside leg while supported by the outside rein/aids are hell to keep straight and I always just go back and retrain the basics that every three year old just undersaddle should know. You can always tell the ones who have been ridden with that outside rein coming forward… the shoulder pops and the horse is never engaged. They are impossible to ride accurately this way. When the horse is correctly bent and stepping into the outside rein you can put them anywhere, it’s power steering at its finest and the possibilities become endless. Perhaps you have to experience it to know what it feels like, to emulate it. There are so many things that cannot be conceived of until you experience them!