https://www.smithsonianmag.com/innovation/shark-skin-inspired-materials-have-a-long-way-to-go-before-they-work-like-the-real-thing-180980973/

Few people have gotten close enough to a shark to pet it. If you could run your hand from a shark’s head to its tail—not that you should—it would feel smooth, almost like suede. Reverse direction and it’s rough like sandpaper. Viewed under a microscope, shark skin is composed of ribbed, dragonesque scales layered over each other like shingles on a roof. These structures, called dermal denticles, are more like teeth than skin

But it’s not completely covered in fur. A partially hairy sphere doesn’t need a cowlick.

A topological sphere so unless moles are actually a torus then it's still not possible.

I dont remember learning about moles in math. Chemistry, yes, but I don't think moles care much about topology.

However, if we assume an ideal mole in empty space with no air resistance, we would see how they have this property: their hair follicles would, in the absence of outside interference, stand straight up. So, its technically more accurate to say that every direction of petting a mole is equally wrong.

It's very short and perpendicular to the skin. It feels like velvet.