For those that don't know...
There is a small clip in the slot you need to push from the other side, this is holding the headrest in place.
Once you remove the clip be careful not to swing the head rest front to back. You will break off the clip ends holding the head rest from flopping around.
Notice the difference between the heads, one has a clip and the other does not.
Look at the end of these two headrest holders, see the ends, they clip into holes in the seat and the only way to get them out is to squeeze them together which you can't do if it's in the seat. That being said if they do break, you need both to break so you'll be able to pull them out the top of the seat.
Dan
PS. if both of those are broken that is why your headrest will wiggle front to back. These usually break if the headrest is hit hard from front or back.