Seat headrest
I would suggest that you remove the headrest entirely.
At that point, you can shine a flashlight down the "tubes" for the headrest.
There are (normally) two little plastic tabs down those tubes, used to keep the plastic trim piece attached to the seat. It's possible that one or more of these tabs has "slipped" out of its' catch and is stopping the headrest from going in.
If that's not it, then you'll prolly have to remove the seatback as others have suggested.
Good luck, hope this helps.