Don't have to be jew or muslim to explain this. It was simply the most humane way to kill an animal back in the days, and some say it still is. When done correctly, the blood pressure drops so quickly that the animal loses consciousness immediately. The entire ritual around their slaughter is meant to make it easy on the animal and bless it.
We also bleed animals to death in Europe, the only real difference is that we stun them with a bolt gun instead of them just passing out from blood pressure, and I'm not so sure I'd pick the bolt gun.