I've been involved in general aviation since the late 1970s, currently commercial/twin/instrument rated, have a degree in aerospace engineering, and do what my username says for a living. So I know airplanes, and why they do the things they do. But an appreciation for what is physically occurring during a stall, how the resulting balance of forces influence the aircraft handling during a stall and recovery, and why the recovery must be handled in a specific sequence to avoid overstressing the airplane or losing directional control, are not intuitive and have never been a very strong point among pilots, or even instructors. As a result, you have poorly educated instructors passing along old folk tales to new pilots, who then take them as gospel.
This has been exacerbated over the years by the segregation of the pilot population into two separate groups, who often receive training that stresses different objectives.
Part 141 flight schools are the typical staring point for airline pilots. In these schools, even when flying little Pipers and Cessnas, stall avoidance is the primary method which is taught. Pilots are instructed to initiate a "stall recovery" at the "first indication of stall", which is taught to be stall warning horn indicator sound happening. The goal is to recover with no loss of altitude, and the technique is to add power to power out of the indicated stall immediately upon hearing the stall warning indicator, and use the elevator to keep the airplane at the same altitude. The problem is that the stall warning horn indicator typical starts sounding about 5 knots in advance of a fully developed stall when flying more or less straight and level. So these pilots never experience a fully developed stall, just an approach-to-stall, and often develop an extreme fear of entering an actual stall. This recovery technique also only works in an airliner in the case of an approach-to-stall or at most a very shallow stall. To recover an airliner from a fully developed stall, you must use the same techniques as you do in a Cessna 172, which is to drop the nose to lower the angle of attach and trade some altitude in for airspeed. This was vividly demonstrated by the five co-captains of Air France Flight 447, who tried to power their way out of a fully developed stall, that could have been easily recovered from by a typical student pilot using Cessna techniques.
I learned to fly in a Part 61 school, which typically are things like flying clubs and independent flight instructors teaching people who mostly fly for fun, or for light commercial use like charters, and will be mostly flying light propeller aircraft. In this environment, the aircraft have a much lower power to weight ratio, you cannot power your way out of even an approach-to-stall. Instead of stall avoidance, stall entry, recovery, and exit is taught. Instead of the goal being to minimizing altitude loss, maximizing aircraft control is taught. The goal is to prevent a poorly-handled stall from developing into a spin, which will usually result in a fatal accident like this one did. So if you learned in a Part 61 school, instead of starting recovery as soon as you heard the stall horn, you kept going until a full stall, and the expectation is that the student would say "STALL" when they identified that the airplane had entered a fully developed stall, based on changes in the handling characteristics and sudden drop in altitude. The student would then initiate a recovery by pushing the nose down to reduce the angle of attack, smoothly adding power and right rudder at the same time to add airspeed and counteract for yaw, and then recover from the resulting shallow dive with no more than 200' loss of altitude, but keeping the airplane under perfect directional control. So in part 61 schools, instead of recovering as soon as you heard the horn blip, you spent a lot of time with it going off in your ear. In fact my instructor used to pull the circuit breaker for it after it went off, as we already knew we were going to be spending a lot of time in an incipient stall condition, and could tell more from the changes in sound of the air going past us than some buzzer. But even in this environment, there are some instructors who just don't like doing stalls, so spend the minimum required amount of time teaching and practicing them.
If you are a pilot who learned in a Part 141 school, or in Part 61 but didn't spend a lot of time in deep stalls, one of the best investments you could make in yourself is to find an experienced instructor and ask to spend an hour doing "Falling Leaf" stalls, where you alternately keep the airplane in a deep stalled condition, and then recover while you really practice your rudder coordination. They're fun! You will loose your fear of stalls and develop skills/instincts that might save you in an situation like this pilot ended up in. You don't need a fancy aerobatic airplane, a Cessna 172 will work fine, but I prefer a 150 because it does not handle like a minivan.
Here's a good video on YouTubes to show what it would typically look and sound like during a lesson: https://www.youtube.com/watch?v=Ocv2YDLk5t0 Note that this is not an example of a perfectly textbook executed falling leaf, it's a student pilot performing them with varying degrees of competence (some good, some not.. keep them ailerons neutral!) and an proficient instructor allowing them to make some mistakes and experiment within the safe bounds of aircraft controlability. So a typical lesson with a good instructor.