Use the correct tools, and they will come out.

Using a drift, you are only hitting one area of the cup, using a head cup remover like this http://www.parktool.com/product/head-cup-remover-rt-1 other brands are available, puts the pressure around the whole cup. Also, make sure you are actually hitting the cup, and the frame doesn't have a ridge in the head tube you are hitting (unlikely, but always possible)

When you have removed the current headset, when installing the new one, would make sure you use anti-seize / grease on the cups to aid removal the next time.