The accepted answer is patently ridiculous...
...but to really get inside Bach's head...
How about looking at Bach's manuscripts?
Here is an example from the Klavierbüchlein für Wilhelm Friedemann Bach which shows a figuration prelude where the completion of the prelude is written out in chords. The idea of chords wasn't alien to Bach or his contemporaries. The answer seems to be mistaking the concept of chords and harmony with the idea of fundamental bass (chord root and inversions) introduced by Rameau which was a new concept for the time. But the suggestion that harmony was not thought of in homophonic terms, as vertical chords, is false. That time period combined contrapuntal and homophonic approaches.
...stacks of exact intervals...that outlook on harmony was a product of the 19th century...stacks of intervals which were the incidental consequence of good counterpoint, rather than purposefully constructed vertical harmonies...
Rameau's Treatise on Harmony describes chords as stacked thirds so the concept is not a 'product of the 19th century.' The figured bass of Bach's time actually is stacking intervals above a bass part. The written figures literally stack intervals over the bass. Realization could be block chords or various figures and textures, but conceptually it was stacked intervals. Here is an example from BWV 151...
But regarding the original question...
We didn't find that A, E and D form a chord...
That is because the chord is actual an
A chord, but the
D note is a suspension.
This passage is actually a perfect textbook example. The previous measure is the "preparation" where the
D is introduced as a chord tone in
i6/4 chord, followed by an
V with the
D note suspended, which then resolved down to
C# for the proper
"Queuing" does capture the essence of the function and handling of the
D note, but the technical term - which the teacher should have known - is suspension.