Right, Joey, it is because of the angle of the shaft to the water. If a paddle enters with the shaft upright, at a 90 degree angle to the water, then symmetrical is what you want. That will present the same square inches of area to force of the water on both sides of the shaft. Therefore, torque on the shaft will be equal, or neutral. A paddler will not experience a twisting of the shaft in his hands.
When you have the shaft at another angle, say 30 degrees, to get equal torque (actually, neutral torque) you need to have an asymmetrical blade. The top part of the blade is not as well covered with water, so it needs to be full sized. The bottom portion of the blade is completely submerged and needs less area, otherwise it will induce torque into the shaft.
When this happens, the paddle will start to twist in your hands, it takes about 3/4 of a second for a human to react, then he often overcorrects. This will be paddle flutter, where the water twists in a direction, and a fraction of a second later you twist in the other. Not a good way to paddle.
If you are serious about a kayak style paddle, here is my experience. A carbon fiber paddle will be the lightest, and most enjoyable to use. Wood is nice, but heavier. If you paddle where you can switch back and forth, you would see and feel the difference immediately. I have long, wooden paddles, short Greenland style paddle, had a very nice carbon fiber paddle.
I now have a Werner Kalliste 220 cm paddle. It is a half pound lighter than the previous paddle. It will cost as much as your boat, and you will grin every time you use it. I gawwr-owntee. (or, something like that)