I had a go with it today, and could NOT get the thing to pop open at all! I inserted and removed it three times with different folds, pushed and pulled, swirled and generally mucked about with it and finally gave up in disgust and turned it right side out again.
I've been using cups for over two years, so I know what's supposed to happen, and I tried all the usual tricks, but I've never used a cup inside-out before. I just tried it today because the LadyCup stem irritates me and I thought I would do this before taking a knife to it. It is hard to remove as it is, and someone mentioned that inside out might be the way to go...
So, anyone done this? And what was the key to making it work??