They way they work is that the string's ball gets trapped between the pin and the bridge plate. I push/repush them in as gently as I can, so they're easier to remove. Also, some pins have bigger heads and are easier to grab with a puller (usually the one on a cheap string winder, right?).

Keep in mind that pulling with pliers can put unnecessary stress on the bridge and the top, whereas a puller uses leverage against the bridge.