Why is casting so important to our art? Some would argue that it is casting that sets apart from the bait or spin jockeys. We would argue that this is not the reason that casting is an integral part of what we do. It is completely possible to fly-fish without more than a simple cast, more like dapping, and Czech or European style nymphing generally don't require a cast. Also, when we think about casting, we are generally talking about dry fly casting since casting with a weighted nymph, split shot, and strike indicator is done completely different. So, it's integral that when we examine this commandment we do so by looking at the traditional fly cast and dry fly presentation.
Unlike bait and spin fishermen, the weight of the fly line is what gets our "bait" out to the fish, whereas bait and spin fishermen use the weight of the bait or spinner to get their line out to the fish. To get more fly line out from the rod onto the water means that we must manipulate the line by putting some type of forward momentum into the line, this means casting. Casting is, generally speaking, what gets our fly out to where the fish are.
As well, the presentation should be as natural as possible. Most of the time a dry fly should find its way onto the water like a "cobweb" falling from the sky, soft and gently, almost without notice on the surface of the water. If it creates too much of a splash or a pop it may scare off the fish that would have taken the fly. Also, a hard cast can actually submerge that dry fly by forcing it into the surface film.
Once again, there's a lot of factors working against a perfect presentation, but we should never settle for letting those factors get the upper hand. Work towards precision, Good Luck and Guid Luck!