It's also important to point out that you shouldn't coast downhill a long way, as down a mountain, keeping your speed using the brakes. You should definitely use the engine for that, as glazing your brakes becomes an issue and could be dangerous.

Otherwise, why would you use your engine to slow down? The brakes are going to do a better job in almost all cases. It takes a significant amount of time to change gears, especially if you match revs to avoid damaging your drivetrain components. Of course, you should also put your car in the correct gear for the speed you're going once you've slowed down, and preferably as you slow down, too.

I'm too lazy to read the whole thing. What was the argument for using your engine?