Okay, I Googled it. I think I got it now, and actually understand why that technique started.
If you were hunting in the woods during the 19th century, you likely carried a muzzleloader rifle that used round ball bullets. It was a suitable weapon that worked for most big game--squirrels were a different story. Shooting a squirrel with a projectile from a muzzleloader would turn the small animal into a pile of mush. So, they had to come up with a way of hunting squirrels without shooting them directly. Alas, "Barking a Squirrel" was born!