Is your mom or dad still driving, even though they are exhibiting signs of dementia or Alzheimer’s? You are not alone! The hardest thing to do with elderly parents is to take away their last form of independence, their car.
My mom was the same way when it came to discussing her driving abilities. 
She insisted she could drive, even though she couldn’t remember things and became easily confused when stressed.
In fact, it wasn’t until she mistook the gas pedal for the brake, and slammed into another car causing a crash before we stopped fooling around and took the keys away from her. It took her several days before she confessed that she mistook the gas for the brake. Before that, she just said he came out of nowhere. Then one day she remembered what REALLY happened.
That remembrance scared her, and for the first time, she agreed with us that she shouldn’t be driving.
The point is, do something proactive NOW, not after someone may die! No, it won’t be easy or pleasant, but neither is the alternatives when you fail to do anything.