Let's look at the Wheel. The wheel is essentially a circle, standing on its rim, and pointing forwards. From the centre of this circle is an across-space, hight axle. In the primitive case, we stand on this axle, and steer the wheel by pulling back on the axle at the side we want the wheel to go to.
In three dimensions, the axle is a line. We might stand on the two protrusions, and steer it, rather like a unicycle.
In four dimensions, the axle has two dimensions, across-space has 4-2 dimensions. Even though we could also turn the axle, it does not do well to do so, since it yields no benefit, and is somewhat dangerous.
To understand this, we need to consider what happens when we look at four dimensions. We note that three dimensions can be regarded as a picture or a map. Let's make it a map, where down becomes forward.
We now imagine that we are falling. This equates to going forward. We steer our fall by pulling on ropes on the parachutes. Pulling on ropes here represent pulling on the axle.
Firstly, we note that while we could spin. Doing so would make it very hard to steer because the same direction would be rotating on the axle. Ideally, we don't want to do this, because if we're going down a precise route, it becomes hard to do so.
Secondly, we note that a group of parachutists would not experience any preference to face any given way. That is, there is no absolute way of selecting 'left' from 'right'. Instead, all we have is 'so many degrees clockwise'.
Riding our wheel down the road, we then try to minimise rotations of the axle around the wheel, and let the wheel do the turning in the up/forward hedrix.