It is not true that whatever a human can do, a machine can be taught to do. The human must have insight into HOW they do it in order to teach it, or otherwise come up with some new algorithm. There are a large class of things humans do that they don't understand the mechanics behind, and for which there also aren't algorithms.

I'm not talking empathy or philosophy. How about just folding laundry. Not just one type, not in a controlled environment, but folding any laundry anywhere.