rodmoe is right, there is a second button that you need to push in opposite the normal adjustment. Its a bit fiddly to operate because it is very small, but if you persist, the headrest comes out of the seat.
....I realize this may be a Zombie thread but while searching for seatcovers - I came across this article - so to help others with their headrest removal, here's a later update with photos to help demonstrate...

Here's an example - to help remove the OEM headrests, Ford Fiesta 2018...4-door Hatchback (or 5-door HB)
Recline the seat back towards the rear for better room to remove the headrest...
First - lift the headrest to full height - Passenger side shown

To do that, press in button you see orange arrow....
Lift the headrest...all the way up until it stops...
It may help to count the notches...
Go to the opposite side...
and locate tab...

Then locate a Philips head tool - like a bit for a variable speed drill for deck screws - something pointy - but not too pointy...
Press that smaller tab in...
Keep the pressure on that tab and using other hand and your arm / wrist...
Continue to apply pressure and push in other side tab to release the posts as a pair
and lift upwards...
This helps release the opposite post from it's last notch
Continue to lift up - and you'll know why you had to tilt the seat backrest back...
The arms are pretty long.
There ya' go!
To reinstall, just do the opposite - tilt seat back, just align the freed headrest to it's forward position, align the poles to the holes, then push in the poles to seat the headrest - evenly - and then you're done!
Now, you can reverse the headrest to the outward curve part in towards the front, but you have little ability to adjust - for the notches that hold the rest in vertical position, won't work well - they are reversed.