What is the origin of the precession of a mounted rotating wheel ?

A simple experiment that most of us have seen or gone through is that
when you tilt the axis of a rotating wheel that rotates in a vertical
plane in a vertical direction while standing on a freely rotating
plate, the wheel will exert a torque upon you to rotate you in a
horizontal direction to keep angular momentum fixed. What is the
origin of this torque? I don't wait for a descriptive answer like:
the conservation of angular momentum, but a more deep answer that
explains exactly how this torque was generated from the deepest level
(or the most microscopic level).

This problem is exactly the same as the precession of a rotating wheel
mounted from a rope from one end of its axle. Gravitational force on
the other end produces a torque similar to the one you produced by
your hands in the first case, and the wheel acquires a horizontal
precession around the robe.

PS. Professor Lewin in his video lecture on MIT OCW mentioned that
this phenomenon is amazing and very non-intuitive.
Thanks

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