Whatever you don't twist the stems with pliers like some posters suggest. Yes, that idea will work, but you'd put scratches on the chrome plated stems and twist the plastic sleeve out of position.
Here's a safe way.
1. Raise the headrest all the way up. As you may already know you can't completely remove it even with tremendous force. There's a retainer clip holding each stem.
2. Grasp one stem at a time pull up while wiggling back and forth until the retainer clip gives way. You can't remove headrest yet because there's not enough room for stem.
3. Grasp other stem and do the same thing. Pull up while wiggling.
4. Once both sides are free from the rear deck, they should slide up from the plastic sleeves with ease.