If this is an EF series shifter the white plastic cable spool has a slight catch that helps to trap the cable head in it's socket. Usually some slight shove and wiggle are enough to release the cable head.

The other way cables can get stuck is when they have been dislodged from the spool's socket and then the spool is rotated. This jams the head between the spool's outer surface and some shifter body inside surface. Again "working" the cable with pushing pressure can often loosen it. Every so often I need to go at the cable/end with a hooked probe. Andy.