Instructors are almost as knowledgeable about cars as taxi drivers. The fact they drive them a lot often simply seems to give some of them a superiority complex.
Modern automated gearboxes are controlled by their own transmission control unit (TCU) which needs to be calibrated rather like (and in conjunction with) the engine management system and of course the two have to talk to each other in the process over the CAN. bus
Automated transmissions are generally hydraulically actuated with the exception of some automated manual transmissions (AMTs) that are electrically actuated. They see to be dying a death due to the awful delays during gear changes and they feel as if somebody is in the car operating the gears. DCTs offer the same mechanical efficiency of direct gearing with almost instantaneous gearshifts which is why they are popular in supercars. There is an extra set of output gears so additional cost and size but that's not usually an issue.
Although they suffer from the need to run a hydraulic pump most of the time, the TCU calibration is much more knowledgeable about the optimal shift points than any normal human driver. Thousands of hours of engine and vehicle test data are used to map out the almost infinite number of shift points that result from changing throttle, load and driver desire ("sport" mode).
Most drivers are pretty much talentless at knowing how and when to change gears for maximum economy or performance. Even so, BMWs have 8 speed autos and there isn't a human alive who could possibly know how to control them optimally themselves, even within the team at BMW. We have a peculiar prejudice in the UK against autos but nowadays you are almost certainly going to have better FC with one, even with the slight overhead of the additional hydraulic pumping losses, the main downside being the initial extra cost.
You'll notice that hybrid vehicles aren't generally available with manual transmissions any more. No point developing a hybrid vehicle with 10-15% improvement in fuel consumption only to have the ignorant driver throw it away through a complete lack of driving talent. Honda Civic Hybrid is an example of that change.
Murray