Why do we call the false self “false”?

Recently Charlie Rose interviewed Dan Harris, a journalist for ABC News, about his book "10% Happier: How I Tamed the Voice in My Head, Reduced Stress Without Losing My Edge, and Found Self-Help That Actually Works--A True Story." Harris, obviously a man of superior intelligence and education, was stunned when he first heard the idea that there is a voice inside us that carries on a boring and negative commentary on our lives, and that meditation could reveal this voice and reduce its power over us. The good news is that mindfulness (or presence) is entering the mainstream, but it was sobering to realize just what we face. When trying to communicate the essential ideas of Sufism, spirituality, and consciousness to a culture so unaware of basic psychological, spiritual, and metaphysical knowledge and distinctions… it is as if we are offering the finer skills of horsemanship to a society where riding a donkey is a new idea (though Sufis also know something about riding donkeys!).