If your sink stopper won't come out, it's likely because it's attached to the pop-up rod and is stuck in the closed position. To fix this, first make sure that the lever on the side of the sink is in the open position. Then, use a pair of pliers to unscrew the retaining nut that holds the pop-up rod in place. Once you've removed the nut, you should be able to pull the pop-up rod and stopper out of the sink. If the stopper is still stuck, try gently tapping it with a hammer to loosen it.