The other parts going on that are unsaid in this:

Your legs and shifting weight are helping to steer the horse while at speed and keeping your balance.

Your off hand is keeping the coils loose and untangled, so the extra rope will play out freely when you throw.

Your off hand is preparing to safely dally on the saddle horn, aka wrap quickly to lock in tension. You can and will get injured if this goes wrong. From severe rope burn to losing a thumb.

Keeping a repetitive motion with a 5 foot loop spinning over your head is helping keep the working end of the rope out of the way, preparing it to throw at the right time, and using muscle memory to help coordinate all the other actions going on simultaneously.

Beyond that, each rope is different as well, some are twisted for left hand vs right hand, some are stiffer, some are well broken in. The force of spinning keeps the loop from collapsing and getting twisted up.