How do I learn to slow down without pulling in reining?

Learning to slow down without pulling requires developing the seat as the primary rate control rather than the rein, and that development happens progressively through deliberate exercises at slower speeds before it is required at the lope during pattern work. The key principle is that slowing comes from the rider reducing the energy output of the seat — sitting back slightly, allowing the hip to follow less actively, reducing the driving quality of the lower back — rather than from taking backward contact on the rein. At the walk, practice asking the horse to slow by becoming quieter in the body: less active hip, deeper breath out, softer lower back. The horse that has been trained to rate from the seat will slow in response to those changes without any rein being applied. When that works at the walk, apply the same principle at the trot and then the lope — the rate cue is the same, just at a pace that makes it harder to apply precisely because the horse's motion is faster. The rein can be used to reinforce the seat cue if the horse does not respond to the seat alone, but it should arrive after the seat cue rather than instead of it, and should be released immediately when the horse begins to respond. A horse that responds to the seat alone needs no rein for rate, which is what makes the ride look effortless and invisible. Building this response requires consistency: every time the horse is asked to slow, the seat cue comes first and the rein comes second if needed. A horse that learns the seat always precedes the rein will begin to respond to the seat alone over time as the horse anticipates the rein following if it does not respond to the lighter cue first.