I've watched the video linked above in the thread and I admit that I was wrong, that I would countersteer when riding a bike, it's just that I don't realize it.

There's just one thing that I don't understand: on a bike, with the hands of the handlebar, I can turn right by leaning right, but I don't understand how leaning right would cause the countersteer left.

It should be recognized that you were willing to admit you were wrong - personally I find nothing in the world harder to do, let alone on the internet. That's awesome.

Here's another video that helped it click for me when I didn't get it either https://www.youtube.com/watch?v=PgUOOwnZcDU It's more "phsyics-ey"

When your hands are off the handlebar and you "lean right," the handlebars won't visibly "turn left," and if they do it will only be for the briefest moment. It only takes the tiniest countersteer to cause the "lean angle." It has to happen because your handlebars are non-rigid.

Let me know what you think after the video above. IIRC it has the "rolling cup" example, which for me works best.

Yeah it was hard to admit I was wrong.

I watched the video above and another one and I'm getting it a little better. Also another thing is that recently I've been riding a bike rather slowly, at speed where countersteering is not necessary and less visible, as shown in another video (https://www.youtube.com/watch?v=C848R9xWrjc). And as for countersteering while the hands off the handlebars, I realise that usually my eyes are on the road, not the handlebars, so I'd easily miss the brief countersteering.

Thank you for your patience too!