Everybody wants their horse to be soft in their hands and tuck his nose in vertically. I know I want my horses to be light and collected more than anybody. But before you can ask your horse to soften vertically using both reins, you have to teach him to soften laterally using one rein at a time. Think of it this way: If your horse resists your hands with 10 pounds of pressure when you pick up on the right rein and 10 pounds of pressure when you pick up on the left rein, there will be 20 pounds of pressure when you pick up on both reins.
Whenever I start training a new horse, whether it’s a colt or an older problem horse, I don’t even think about picking up on two reins for at least 10 days to two weeks. In other words, until I’ve gotten the horse extremely soft laterally. I should be able to flex his head from side to side using just two fingers on the reins and be able to do a One Rein Stop at the walk, trot, and canter by just picking up on the rein with the lightest touch. Once the horse is that soft laterally, he will catch on to vertical flexion easily.