Rabbit hunting is small game. Small game is very challenging. Obviously not so dangerous. I haven't heard too many people get attacked by a rabbit lately.
But it gives you the opportunity to show your perfection with the bow. It shows your training. Training with the bow to go after rabbit, you want to train on a moving target, of course, because very rarely you're going to find a rabbit that's just sitting there waiting for you.
They can sense your presence from a long way off and then they'll just take off. If you happen to see a rabbit and take the shot at it, you're a good shot because a rabbit's not a very big target.
It's a trophy that you can brag about, I guess. But you've got to be a good shot to shoot at a rabbit. It's fast and it's small.