It can be a timing issue.
Many times in this situations the horse doesn’t actually complete the transition. For a halt transition, they might stop their feet, but the rider should maintain the pressure until the horse ALSO says “yes” to the halt by relaxing its neck and softening in the contact. For a horse that is new at this, that can mean keeping the rein and leg on for 15-30 seconds after the horse has stopped his feet. The halt isn’t done until he relaxes and if you float the reins, he stays put.
That said, asking for real halts can be a real mind f*ck for an anxious horse, and if it’s not done very tactfully and calmly, they can get upset about it. For this reason I try not to do halts at all until the horse is ready - and bad halt where the horse is still leaning on the bridle and immediately surges forward the second the rein is released just trains more anxiety and less waiting into the horse.
For the OP, I recommend keeping your leg on, always. Many people on quick horses take their leg off, and then the horse is kust waiting for the leg to come down from the sky again when the rider wants something. Keep the leg ON (I think of it as an “embracing” leg).
My horse can get claustrophobic to the aids and his response to contact was initially to bull dose through it. Anne Gribbons told me “PUT DE LEG ON! DO NOT LET GO DE HAND!” so basically I put leg on, maintained the rein contact, and proceeded to porpoise around an Anne Gribbons clinic for 45 minutes until my horse came to his own conclusion that it was easier to just accept it. The key was NOT ESCALATING with the hand (just keep it the same and let the horse figure it out) and releasing the INSTANT a small measure of acceptance happened.
However once you start you need to be committed - if he starts porpoising and then you say “This is more than I bargained for” and abort mission, he’ll learn that if he just escalates, that’s the ticket to getting what he wants. So then you’ve trained him that escalating at you gets him what he wants.
The release is also the absolute most important thing. Many people if a horse is working things out with four legs in the air the last thing they want to do is release, and then you’ve put your horse in a no win situation where his only option is to fight you to the death. So you need to have a pretty good sense of humor, not take anything personally, put same sticky on your breeches and be prepared to just wait it out.
