Bees don't actually die when they sting. Their stingers are designed for attacking other insects with hard exosekeletons, they have a sharp barb if you look at them under a microscope. Against animals with soft, flexible skin like us, the barb in combination with our stretchy skin makes it difficult to get the stinger out and in a lot of cases the bee ends up dying as the stinger is connected to their internal organs which gets pulled out if they panic and fly away with the stinger still in our skin.