How to explain to someone with no knowledge about Buddhism what is meant by "extinguishing" the self?

A person I know has drawn the unwanted conclusion that the entanglement from the self is to be equated with erasing one's personality, feelings and connections in life. That to be extinguished in Nirvana means the complete loss of the contents and meaning of one's life and forever remaining in a state of unfeeling lethargy. I have not answered this person yet for I don't know how. It happens to most Westerners at some point. It's very hard to grasp Buddhist concepts. Could someone give me some advice on how to explain to that person what Buddhists mean by the extinction of the self?