Some people's hair really does stop growing at a certain length. If body hair didn't stop growing by itself, we'd all look like King Kong.
Hairs have a life cycle from start through growth to falling out.
When a hair has reached the right time to fall out, it falls out, no matter how long or short it is by then. Body hair's growing phase is much shorter than that of the hair on your head. And scientists still don't know why that is. But body hair has finished its growing phase much faster than the hair on your head. The average person loses about a hundred hairs a day.