A horse that has learned to push through pressure — that leans into the halter rather than yielding to it, that increases speed rather than softening when the rein contact increases, that pushes against the handler's hand or leg rather than moving away — has been trained, whether intentionally or not, that pushing produces results. The fix requires going back to the beginning of the pressure-and-release concept and retraining the association between pressure and the direction of the desired response.
The first step is reducing the intensity of the pressure cue so that the horse is not pushing into something it already has a strong defensive response to. A horse that pushes hard into strong halter pressure may not yet push against very light halter pressure — starting there, at a level below the horse's push-through threshold, allows the horse to discover the yielding response without immediately triggering the defensive pattern.
The second step is ensuring that the release comes only when the horse moves away from the pressure, never when it is pushing into it. This requires discipline from the handler — maintaining the pressure through the push, which may be uncomfortable, and releasing only when the horse softens even slightly. The release must be immediate when the softening occurs, because the window between the first try and the horse giving up on the try and pushing again can be very short.
For horses that push through rein pressure under saddle, the inside rein bend-and-release technique is often effective — applying inside rein contact, bending the horse's nose toward the rider's knee, and releasing the moment the horse softens rather than trying to maintain contact through a bracing horse. The bend prevents the horse from using the full strength of its neck to push through, and the release when softening occurs gradually teaches the horse that softening to the contact produces the release it is looking for.