Breakaway halters are useful if you have a horse that has to wear a halter all the time. The most common reason is because the horse bites. If he’s already haltered, you can snap a leadrope directly to the halter while standing at his shoulder, where you can deflect a nip. I also use a breakaway halter on Prim, my old mare with the dropped fetlocks, when I turn her out to self-exercise. (She never lets Gunsmoke out of her sight, which is the reason I turn him out in the arena first.) When I let go of her leadrope (a very short one, called a “catch rope”) and cluck, she gallops towards him and they circle the arena a couple of times, Gunner on the inside, Prim on the outside. It’s short, so she can’t step on it and trip, or get it snagged on something. Even if she did manage to do that, her breakaway halter would do its job and break. Unlike Gunner, she doesn’t wear it all the time—just when I turn her out.
The cat who nips at your hand is similar to the horse who nips at (air bites) your hand, and you can use the same methods to stop the behavior. Keep your hands away from his face; never allow him to play with your hands; and never, ever, physically punish him.