brads or finishing staples tend to be set below grade on wood. if you back them out the way they went in, you have about a 100% chance to blow out a chunk of wood on your finished side.

use end nippers, needlenose vice grips, or channel locks to pull them through the rest of the way. the staples/brads are designed to go one direction.

if you’re pulling them out of another finished side, you can use a flatbar under your nippers to protect the wood and roll against the flatbar. you could probably use some thick leather or rubber too.