When raw hides are dried, the nails are placed very close together to prevent a rough edge like that.
The greater the distance between the nails the more ragged the edge will be.
You can try wetting the leather, tacking it out on a board and leave your nail spacing about 1 1/2 to 2 inches and allowing it to dry over night.
Try it on a small piece to see if you get the results you're looking for.
Once the leather is tacked down raise it on the nails to allow the air to get between the board and the leather.