From my amateurish reading and thinking about the subject, it's rather our ability to explain things and we don't know yet how we do that exactly. That's also why they should just have mentioned the neocortex instead of the (as yet not entirely understood) source of creativity. BTW, understanding where this capacity to explain comes from would also enable us to create true AI.

Many animals communicate (albeit with a much more limited vocabulary) and classify things (although much less flexibly, according to predefined criteria).