Although this is a pretty old topic, it is at the top of the search results for removing Stick Coils. This should probably end up in the Wiki at some point (Jim?).
I fought with mine on a recent valve inspection, and after reading this, didn't see where anyone clearly communicated what's going on (though lots of comments are really close).
The problem is the rubber around the coil is sticking to the valve cover and / or head. Until you get the rubber boot around the stick coil to rotate, not just the stick coil itself, it will not come out (at least easily, or in one piece). This is why grease will help in the future, but if the factory failed to grease them adequately for you (like they did on #3 for me), the first time is a PITA.
For the ones that were greased, I found that applying pressure with my fingers to the rubber just below the connector, while rotating the coil, allowed it to break free. Once that was achieved, continuous lifting force (still with fingers only), while rotating back and forth, popped them out.
For the #3 in my situation, nothing I tried would turn the rubber part. I actually tore part of the rubber trying to get it to move. Finally I used a small pick / probe, with a 90 degree bend on the end, and worked it around between the rubber boot and the valve cover. Eventually I was able to free it, and get it to move. This is where some WD-40 would help as well (between the rubber and the valve cover).
Attached are some pics to show the newbies out there what the stick coils look like. When fully inserted into the engine, only the connector portion at the top is visible. A close look at the first pic, second coil from the top, shows where the rubber tore on mine. Also notice, that's the one with no grease.
When greasing, I would apply to both the bottom area where it's visible in the first pic, as well as the upper ribbed section. The upper rubber section ends right about even with the tip of the spark plug in that pic. You can see the seam on the first (top) coil, where the color changes slightly. When the rubber is stuck, the coil will rotate inside the rubber to that seam.
I also numbered mine when I removed them. They're interchangeable, but I'm just picky that way (anal?). I used some hot pink fingernail polish, in case anyone is curious (left over from marking red lines on Pyrometer gauges
).
Hopefully this proves helpful to someone in the future.