The way I learned to swim was pretty interesting, I remember the moment pretty clearly because of the absolute shock of fear at the time -- but it was a rather interesting method. I don't remember if the teacher tried to teach me in the same failed way you're talking about here to being with -- but whether she did, or didn't, I couldn't swim. I was pretty young at the time, so the surrounding memories are a little hazy -- though the moment itself is quite clear.

So since I couldn't swim, and couldn't figure out how from explanations, the teacher had me pushing off from the wall and grabbing onto this floating barbell thingy -- no swimming involved, except for bringing it back to the wall, which I could do because I had something keeping me from going under. I'd then push it away from the wall, push off the wall and grab it, and do it again. The teacher had to fetch it a few times, because it got too far away for me to get to in one push.

Then one day (I don't remember how long I did the push-off-the-wall thing) I was proceeding as normal, and the teacher came along to watch. And I pushed off the wall again, as hard as I could, to grab the floating thing -- and she grabbed it and pulled it back. And with what I realize now was probably a shock of adrenaline, I swam towards it. And she swam backwards with it, and I kept swimming towards it. It was a horrid doggy paddle, of course, but I was swimming.

I don't think this is an effective method for most things, and it might not work for some people, but it certainly worked for me, in that situation. Problem is, I can't think of many other situations where it would be effective -- bike riding is the only other skill I can think of where this method might work. Can anyone think of anything else?