We would have got lost if it the map

"Vanishing" has the connotation of happening almost magically-disappearing while people are looking. It also shows that something is disappearing or ending very quickly. Something 'finishing' or 'ending' feels like it was supposed to happen, that it's nothing out of the ordinary. Vanishing has a much more extraordinary quality. 

This supports his main idea because he is trying to prove that terrible things (like the Holocaust) happen right in front of people's eyes and they don't do anything to stop it if they are being indifferent. This ties into the act of something vanishing because it happens in magic when people are looking right at the magician or the object that disappears.