If you look at your curb bit, every inch of the curb shank adds more pressure to the horse's mouth. So, a 3 inch curb bit means that if you pull with 1 pound of pressure, 3 pounds of pressure is put on the horse's mouth. If you pull with 5 pounds, then you create 15 pounds of pressure in the horse's mouth. Now, with that math in mind, can you image how much the force of your hands is multiplied when you yank on a horse's mouth? A 10lb pull is about 30lbs on the horse. Now, I'm not trying to make you feel any worse, but with a snaffle/halter/bosal, you get a 1-1 ratio. That means you pull 1, you get 1. You pull 5, you get 5.
One of my main objectives when I ride is sensitizing the horse to the bit, and being aware of the pressure I put on him. If I were to constantly ride with 5 pounds of pressure in his mouth, it will take me 10 pounds to get him to react, and so on and so forth. So my goal is to ride with 0 pounds of pressure in the mouth until I want a direct action from him. Then my goal is to only use maybe 1 pound of pressure, and then less and less. And this is in a snaffle. I want no more than 2 pounds of pressure ever on my horses mouth when I am going in a very collected frame - which means I get to hold in a snaffle, and barely touch the reins in a curb. And for western pleasure and english pleasure, I essentially want tiny, tiny increments of pressure to achieve my headset. The rest I do with my leg.
Now, to sensitize a horse, you need to think of pressure and release. When you start in a rope halter, pull your horse's head to his side and hold with steady pressure until he "dips" and give a big, immediate release. How much pressure did it take for you to pull his head around? How long did it take until he sought the release? If you had to pull hard and wait a long time, your horse is not sensitive to seeking that release from your hands. You need to teach him to seek the release and the less pressure he will have. I want to do this exercise so much on the ground and in the saddle that all I need is a pinky's amount of pressure for my horse to turn his head and "give". This will help immensely with hip disengagements, and getting your horse's attention back.
A horse that is stiff in the neck is stiff in the body, and stiff in the mind.
You will immediately see a great change in the way your horse reacts to a simple snaffle bit.