In 3d an object that is moving forward has two degrees of freedom that could cause it to go off course. It could go vertical or sideways instead of moving forward. In 3d spinning around in circles that are perpendicular to the direction it is moving forward in helps to stabilize the object and helps it to move straight.
In 4d simply spinning an object moving forward would have one more degree of freedom from an object moving forward in 3d. In 4d if an object that was moving forward was to spin in circles perpendicular to the direction it was moving forward in then it would still have two degrees of freedom left over that could cause it to move off course. For instance if an object was to spin clockwise or counter clockwise the Ana-Kata directions would be left over to destabilize a corkscrewing object. In order for an object moving forward in 4d to use spinning to stabilize it would have to spin in spheres perpendicular to the direction the object is moving in.
In 3d it is impossible for an object to have two independent directions of spin so in 4d it is impossible for an object to corkscrew in two independent directions. It would take five dimensions for an object to corkscrew in two independent directions as it takes 4 dimensions for an object to have two independent directions of spin. It is still possible for an object to spin in multiple directions in 3d but the directions, just not in two independent directions.
In 3d if the polls of none rotation move slightly from their original location after each spinning cycle and if they keep moving in the same direction a second direction of spinning will be produced. So while it is impossible to have two independent directions of spin in 3d it is possible to have an object spin in two directions in which the second direction of spin is based on the first direction of spin. So in 4d it would also be possible for an object to corkscrew in spheres for stability.