One driver tells one story, while the other driver tells another story. Fault cannot be accurately determined, so fault is divided equally between both parties. In some cases, drivers, police, or insurance companies cannot determine fault. In these cases, you have several options.
Some drivers choose to resort to arbitration, which is a means of resolving the fault without going to court. A neutral referee is chosen to decide the percentage of fault for each driver. Determining fault in a car accident isn't always that obvious. While two parties can assume some level of liability for an accident (both are at fault), it is much more likely that the negligence of an individual driver led to the accident.
Even if you are only 1% at fault, you cannot sue another person for a car accident in the states of Alabama, Maryland, North Carolina or Virginia “pure contributory negligence”, as well as in the District of Columbia. You'd be better off doing this not so much to prove that it's not your fault, but rather to gather the information from the driver's insurance company, which you'll need when it comes time to file your car accident claim. But in other types of accidents where the cause and effect relationship is less clear, you want to take appropriate steps to prove that you are not at fault for the car accident.