Because information cannot travel faster than the speed of light. A rigid body is one in which the distances between every atom are fixed and do not change. But if we gave such a body a push from one end, information would have to travel through the entire body instantaneously to signal to all other parts of the body to 'move'. This means information has to travel faster than light which is precluded by special relativity. So, rigid bodies cannot be described by special relativity, and therefore do not exist in the physical world.