Imagine you were making a ladder by sticking together a bunch of identical blocks, each of which was half a rung and the attached bit of rail. But imagine the rails aren’t perfectly straight—each one is a little bit skewed, so when you join the two halves of each rung the connected rails skew in opposite directions. When you add the next rung the skew of the rails will continue, but the rotational symmetry of the rung will keep it centered over the previous rung. The net result will be a skewed helix.

It might help to look at the actual structure of the molecule—you can see how the sides of the “ladder” are made of a lumpy sugar bit that has no reason to stack directly on top of itself. Also notice that the halves of the rungs vary in two ways: there are long and short pieces, and there are pieces that connect with two or three connections. These two variables give a total of four possible half-rung types, and each can joint with only one other type (long to short, short to long, two to two, and three to three).