This explanation has probably been independently 'rediscovered' many times, and it is unlikely to be able to point to a particular origin.
Ackroyd says in 'Babinsky's Demonstration: The Theory of Flight and Its Historical Background' (Journal of Aeronautical History, 2015):
Imagine that two adjacent air elements ... A and B ... are about to
reach the aerofoil’s nose. Element A passes above the aerofoil whilst
element B passes beneath. Eventually element A reaches the aerofoil’s
tail or trailing edge and element B, according to this argument, must
reach the tail at the same time so as to regain its position adjacent
to element A ... this flawed explanation of flight has survived and
still enjoys wide belief, probably because it has the appeal of
simplicity. Its origin now seems to be lost in the mists of time
although it may be that its use in aircrew training manuals gained for
it a popularity which extended to school textbooks and even the
occasional British A Level examination paper.
Some sources say this explanation is sometimes used in flight training manuals.
The above explanation is extremely wide-spread. It can be found
in many textbooks and, to my knowledge, it is also used in the
RAF's instruction manuals.
Source: Holger Babinsky (2003). How do wings work?. Phys. Educ. Vol. 38. p.498.
Ballow speaking about his experience when learning from Air Force training manuals while a member of the Nevada Air National Guard:
The training covered the theory of flight as outlined and explained in
the Air Force Training Manual [...] Lift is generated by the air
passing over the wing. since the upper surface of the wing is curved
and the lower surface is straight, the air passing over the upper
surface of the wing has farther to travel, and so it is thinned out.
Source: Tom Ballow (2005). The New Science of Flight and Movement. p.13.
Discussion on the r/flying subreddit:
DPE used the 'equal transit time theory' of lift as the correct way to explain lift. What do?
Posts on Aviation Stack Exchange:
Why is the wrong explanation of “air travels a longer distance and creates a lift” so popular?
Principle of aerodynamic lift: are misconceptions also taught in flight schools?
Here are some specific instances of where the "equal transit-time" argument is used.
The distance over the top of the blade with the angle of attack is
greater than the distance along the bottom surface of the rotor blade.
Air molecules that pass over the top must move faster than those
passing under the bottom to meet at the same time along the trailing
Source: Federal Aviation Administration (2012). Helicopter Instructor's Handbook, Chapter 3 Aerodynamics of Flight. p.2.
The shape of a wing looks like an elongated water drop laying on its
side ... Usually the top is curved more than the bottom making the
upper surface slightly longer than the bottom. Since air passing over
the top and bottom must reach the rear of the wing at the same time,
the air passing over the top must not only travel faster, but also changes direction
and is deflected downward.
Source: DoD 101 - An Introduction to the Military, Aircraft for Amateurs
The next examples are from older journal papers.
This acceleration of the particles over the top side of "the shape"
will hasten the upper air-particles toward the trailing edge, so as to
make them "join up" with their immediate bottomside neighbors, from
which they were separated at the leading edge. Particle pairs thus hit
the leading edge together, are separated, and yet arrive at the
trailing edge together—although the topside particle had to travel
much faster to do so.
Source: Norwood Russell Hanson (1965). Aristotle (And Others) on Motion through Air. The Review of Metaphysics, Vol. 19, No. 1.
If we consider a wing passing through stationary air, the principal
effect on the air is the downward thrust. To the approximation that
this is the only net effect, the time required for passage over and
under the wing is the same. The air above must therefore be traveling
faster (relative to the wing) to keep up with the lower streamlines.
Source: Robert P. Bauman and Rolf Schwaneberg (1994). Interpretation of Bernoulli’s equation. The Physics Teacher Vol. 32. p.485.
As for why "equal transit-time" ever had to be invoked.
I could not find any physical justifications for it, perhaps its surface level intuitiveness stems from being conflated with some kind of continuity equation/condition, almost as if air parcels split at the leading edge, must rejoin at the trailing edge otherwise there would be a "build up of air" on the side with the longer path (the "equal transit-time" requirement is of course not necessary to avoid this). This Quora question seems to suggest there is some confusion related to this: Why continuity equation must be followed by aerofoil?