I tried to drive my friend's Spyder (the Sport model) and had to yell to him to get me off the thing cos I'm so used to leaning (and thus also countersteering) that I ended up going the opposite of how I wanted to go and nearly went up the curb.

Countersteering is one of those things that you already do intuitively. If you aren't already aware of it or are just beginning and try to overanalyze and force it, you could very easily go too far and, as DickO mentioned, even go down. I remember reading about it in the MSF manual and wondering what the heck it meant. Once I was on the road, I forgot all about that stuff, and then only later remembered reading about it and then realized that I was already doing it. If I'd just tried to do that from the very beginning, especially at low speeds, I would probably have fallen.

I have ridden with another person who is unable to master the subtlty of countersteering.

I think this occurs due to fear and I have stopped trying to correct her, as she believes she is riding with a lean.

It took a while to lean/counter-steer my silver wing. I would slow down on twisties. It seemed like it took a long time to get really comfortable swaying with the road. Now I don't even think about it. But I'm not at that comfort level on my ninja yet, as much as I'd like to be.