Jump Starting a Dead Car Battery?

So I decided to look at video tutorials on how to jump start a car, as I never knew how and figured it would be a good thing to learn. Anyway after watching three different videos, the instructions clearly state that the working car should be turned off during the entire process. Why is this?

I ask, because every situation I've ever seen, the live car keeps the engine running to send power into the dead battery. I have a friend who is a mechanic who even does this, is it dangerous? I've never seen anything bad happen from it, but since the videos I've watched say otherwise I am assuming I shouldn't do it?

I guess I just don't understand how there's enough live juice to jump start a dead battery if the live car is turned off.

Suggestion:

CONNECTING THE CABLES>>>
Jumper cables have two colors, one side red and the other side black. They have two clasps at each end, two for the red side and two for the black side. The red side is for the positive end of the battery, and the black side is for the negative end. When you locate your battery, you'll notice two posts labeled (+) and (-) (+ for positive, – for negative). Take one end of the red clasp and attach it to the dead car's positive battery post. With the live car still turned off, attach the other end of the red cable to its positive battery post. Now attach the black clasp to the live car's negative battery post. This should leave one clasp hanging free, the other black clasp near the dead car. Do not attach this clasp to the dead car's battery. Attach it to a metal area of the car (one that does not have any paint on it, like the manifold).

JUMPING THE BATTERY>>>
Now that all four clasps are in place, start the live car. Let the live car run for a couple minutes, and then you can start your dead car. Once it's started and running, carefully disconnect all of the cables (never let the metal of the clasps bump into each other if some clasps are still on a battery). Start with the black clasp on the formerly dead car, followed by the black clasp on the live car. Now disconnect the red clasp on the live car, finishing with the red clasp on the formerly dead car.
But don't shut off the engine of the formerly dead car too soon. Make sure it runs for about 15 minutes before you turn it off. Otherwise, the battery may not charge itself and you'd have to do another jump all over again.