A single-bevel saw can be turned only to the left or to the right side because of a massive engine block. In double-bevel miter saws, the engine is placed on the backside of the saw head, so it can be easily rotated on both sides.
It's much easier to work with double-bevel saws because you don't need to shift a wood piece every time you change the direction of the cut. Just rotate the saw head instead.