Balanced view:
the way we turn on a bike is counter-intuitive. That is, we actually give the bike a little counter-steering and the bike naturally falls to the other side - bingo we have lean.
It is why learning is so difficult relative to your intuition.
And watching racing motorcyclists gives a clue to counter-steering, they need to turn quickly. Mind you you have to see it on slo-mo.
It is all to do with the position of the front axle relative to the line of the steering head joint. Have a look at regular bikes, then look at a mountain bike. The amount the axle is forward is less on the mountain bike because fast turns are needed and suspension dictates forces are fairly direct. But is harder to ride. Certainly to learn on.

I was observing a girl learning recently and her kiddies bike was not conducive to her learning, the front axle was not far enough forward. And when she turned left she invariably fell over right, because she wasn't counter-steering, she was "I want to go left, I need to turn left".

Simply put, because even those that study this can't fully explain it:
the front wheel contact point with the ground (relative to the line of the headstock) is modified by turning the handlebars which tends to cause lean.