I'm assuming it's the old plug and removing it that you're having an issue with?
If so did you check to see if when you pull the spark plug wire off that the metal clip inside the boot on the end of the wire that clips onto the spark plug was still on the wire, if not it's possible that the clip has separated/pulled loose from the old spark plug wire and it still clipped onto the old spark plug making it too long to fit inside the socket, it also could sorta block you from seeing the ceramic part of the spark plug.
Look inside the boot of the old spark plug wire and see if the metal clip is still attached in there.
If it's gone that explains why you can't get it to clip back on, you might be able to use a pair of long reach needle noose pliers to reach the clip on the old spark plug and pull it off so you can get your socket on the old plug.
Edit: Here's link to the pliers.
11 in. Long-Reach Needle Nose Pliers