This is one of the most important steps in the removal process if you find yourself needing more than light taps.

The frond of the frame is pretty light so there's a limit to the amount of energy you can put into a blow without the frame rolling with the punch, so to speak.

Stand a 1/2" thick board in a vice, and brace the lower head lug (or welded joint) against it and the cup will move. If you want to drive it straight out without buying a special tool, find a coin or disc just slightly smaller than the head tube (about 29mm, or 33mm, for 1" or 1.125" headsets respectively). File flats on opposite sides forming a "racetrack oval" so you can slip it up into the cup. Once in it'll flop and brace across the cup so you can drive the cup straight with a punch.