Why does airspeed change when I adjust the prop?

He is, of course, right. Pilots often do act on "voodoo" when it
comes to engines, and other flight details. Or at least on the tales
their CFIs told them... some correct, some not. How many times have we
had someone here say "I was told this", and half the replies are "but
no, it's really that!" It's often hard to sort the wheat from the
chaff, not least because there can be so much difference between
airplanes.

No, he is not right at all. There are a few "rules of thumb" that work for
basic training aircraft--which are specifically manufactured to be tolerant
of those practices. However, flying most modern trainers, you can improve
both performance and economy if you operate them "by the book."

The more sophisticated the engine, the more important important it is to
operate "by the book." Geared engines and controllable props are excellent
examples.

In short, you are attempting to defend the idefensible.

It's only fairly recently that researchers outside of the engine
manufacturers really began looking into how the motors work in
practice. And we needed those outside people because for a long time
the manufacturers had conflicting advice, or no advice at all. If it
seems strange at times to pilots, it must be doubly strange to a
non-pilot. Anyway, we all know about GAMIjectors as one example of
research. Here's an interesting read:

That's not true. Most of this was known and documented during (and a lot of
it prior to) World War II, and much of it is documented in old NACA reports.

GAMIjectors are not an example of new research, but of the evolution of
market forces. The relative costs of fuel, certification, and precision
manufacturing reached a balance at which some investors saw an opportunity.
I have no idea whether others saw the same opportunity at an earlier date
and failed in their marketing, or simply ran out of money--but the
underlying knowledge had already been in the public domain for decades.

Peter