The theory of everything

Or maybe it's nothing. Anyway, the NY Times has a nice article on string theory. Could someone explain to me something? How can strings be the building blocks of the universe if they can (they think) snap? If they can snap, they're divisible, hence not the smallest unit. I'm sure there's a good explanation for this, but I don't see it. Actually, I'm not sure that there's a good explanation, but if there is, please let me know.