Originally Posted by
Chombi
I suspect that theres a ledge of aluminum oxide hooking on to more corrosion, that's keeping you from pulling out the post, but letting you spin it. You have to break up that corrosion ledge with some impact force and additional doses of penetrant. Find something metal to hook on to the head/clamp assembly of the post and hit it upwards (or downwards, depending on the position of the frame) with a dead blow mallet, to break up the corrosion further and pull out the post.
My own experience suggests Chombi is right, and Velognome's following quote does also explain the seatpost behavior I've seen:
"Think ya cut a ridge into it maybe? Tap it in and it should twist back out."
I've used toe straps (several as needed) to hang frames by their stuck posts from an outdoor stair-rail, hanging from the post head.
I can then have a large helper put a hundred or more pounds of gravitational force on the frame, so that my further post-twisting efforts cause the post to move vertically.
I've even done this by myself, but the gymnastics were abusive to the old sleleton to say the least, leaving me with wrist soreness and bruises from the frame slapping around while I pushed down on the bb junction with my foot while twisting the post with an 18" adj wrench.
The posts always came out.