Who is right, me or my dad?
He lives in the mountains of North Carolina, and when I go to visit him, he always likes to drive me around and show me the sights. The trouble is, when he drives those narrow mountain roads, he keeps the automatic transmission in overdrive and rides the brake with his foot. I try to tell him that he ought to shift down to drive or second gear, but he insists that I am being ridiculous.
You're absolutely correct. Downshifting, which allows "engine braking" to control the vehicle's top speed, is the best way to drive on steep terrain. Engine braking uses the engine's compression to apply resistance to the drivetrain.
Dad's method of staying in high gear and riding the brakes can be dangerous. Eventually, overheating the brakes will cause brake fade -- the linings get so hot, they can't grab the rotors and/or drums sufficiently to stop the car. The brake pedal will feel hard but, no matter how hard you push, the car won't stop. In extreme circumstances the brake fluid will boil, the pedal will go to the floor and nothing happens.
Tell your dad that he's missing some beautiful scenery by going so fast. And if he keeps it up, one day he won't be able to stop when he is going down a steep decline. This could ruin his view permanently.
As far as the transmission is concerned, select a gear that maintains the downhill speed you desire (first gear if necessary), and use the brakes only when you have to.