The main reason why is due to car design. Newer cars, from mid 1990's and up, are being made with stiffer frames and chassis to better withstand higher speed, more serious collisions. As a result of this increased vehicle rigidity, at lower speeds the car does not absorb any of the impact, instead that force is transferred directly to the occupants. Another big factor is that 75% of Americans don't have their head restraint positioned properly. In fact if your head restraint is too low it will actually increase your risk of whiplash. Many times with these low speed car accidents the onset of pain is not immediate and usually appears within several days or weeks after the accident.
Numerous research studies have shown that there is absolutely no correlation between vehicle damage and risk for injury. Newer model cars are also typically made to withstand collisions up to 10 mph, and sometimes higher speeds, without causing any property damage. A recent study showed that the majority of injuries sustained from auto accidents had no vehicle damage.