LOL The very first fiber I ever 'spun' was cat hair, and I was rolling it down my thigh trying to get it off! It made a rather odd little yarn that way. But I wanted to do *something* with the half pound of shed fur my domestic shorthair cats give me every spring, so when I took up spindling I tried spinning with the fur. I often joke that once you spin cat hair, everything else is dead easy, but I actually found it a bit easier than cotton to spin because of the crimp.
My cats have a definite crimp to their fur, and I have no trouble spinning it alone, but very straight or hairlike fur would be a lot easier to spin if blended with another fiber. That's true for most of the short fibers, and some of the long ones.
It's a lot like spinning cotton, angora, or any other short-staple fiber. It spins okay on a supported spindle but is really tricky on a drop spindle. I have made about 57 yards of lopi-style yarn with just their fur from last year! It fulls slightly when wet-finished and thwacked, and I like that finish a lot. I've also tried blending the hair with alpaca and recycled silk with fair results (dunno where that yarn is to photograph it).
This one is cat fur yarn in progress on a very light homemade spindle.
This very blurry one is the wet-finished yarn.