stillsostrange

Actually, you do have to kill the silkworm:

If the animal is allowed to survive after spinning its cocoon, it will release proteolytic enzymes to make a hole in the cocoon so that it can emerge as a moth. This would cut short the threads and ruin the silk. Instead, silkworm cocoons are boiled. The heat kills the silkworms and the water makes the cocoons easier to unravel. Often, the silkworm itself is eaten (see Cuisine). (http://en.wikipedia.org/wiki/Bombyx_mori)

Still, silk is not made from the formerly living tissue of the worm; like wool, it was never itself alive. So I agree that the leather thing totally makes sense.