Aliens
Some conspiracy theorists hold belief that the locals built the buried city to protect themselves from alien invasions. Yes, you read that right. Aliens were as much a worry as they are now, apparently. The logical explanation offered was that if aliens had tried to invade, they would be able to hide. To this day, there are alien enthusiasts who regard Derinkuyu and the area surrounding it to be a perfect spot for an alien invasion.
Natural Disasters
The exact date that the city was built is unknown and therefore conflicting views bring up the next theory. Some theorize that this was a shelter during the Ice Age period. Others disagree and argue that the shelter protected the population from natural disasters that came much later.