1: Panic. His brain's "we're falling out of the sky" alarm was louder than the plane's stall alarm. (The correct reaction to the first is the opposite of the correct reaction to the second.)
2: Mental error caused by UI confusion. "Stall speed" is shown on the airspeed indicator, and he knew his airspeed sensors had failed. Therefore, he concluded that the stall warning was wrong. (But, stall is not detected by the pitot system, it's detected by angle-of-attack sensors which were working just fine.)
3: Training. Pilots are casually taught "you can't stall this plane" because under "normal law", that's true. No matter what input you apply, the computer will not let you stall the airplane. Unfortunately, the plane was not in "normal law" at the time, because of the failed systems. (This is indicated somewhere, the information that the plane's not in normal law is available to the pilots.) I'm guessing that no instructor ever mentions those exact words in bullet-point form, but I'm guessing that someone has said, "just pull back as hard as you can, you can't stall this thing" when practicing, say, engine-out-on-departure procedures. And statements like that stick.
This has been mentioned in other articles about the crash, including ones that have been posted in HN.
Under normal conditions, when the flight computer is receiving airspeed and other telemetry normally, the fly-by-wire Airbus operates under "normal law", a mode where the pilot controls the aircraft but the flight computer prevents stalling and other dangerous situations. In this case, the pitot tube was frozen and the flight computer didn't receive proper airspeed data and went into "alternate law" mode, where the pilot controls the craft and there are no computer enforced limits. The co-pilot with the controls had probably not flown the aircraft under alternate law or incorrectly believed that he was operating under normal law, and had never heard the stall warning before. So either he thought that the stall warning was false and just another instrument malfunction or he just didn't understand it's meaning in the confusion.
The flight mode is important but not the reason why they crashed the plane (IMHO). The reason they didn´t do anything else but pull the sidestick and apply TOGA was that they thought it was the solution to the problem.
The problem to them was thunderstorm + fast speed variation (unreliable speed indication or no indication at all)+ autopilot disconnected.
So they applied one of the most practiced maneuvers in commercial airplanes simulators the wind shear which is one of the most dangerous situations an airliner could face, and therefore one of the most practiced maneuvers(due to economical reasons refresh simulators are more and more condensed and reduced, almost no time for "basic" maneuvers like real stalls, regular manual flying, etc...).
Usually severe wind shear takes place in the presence of thunderstorms (they were flying inside one ), then there is a severe change in speed indication and wind speed(also present at the AF flight) How do you fight a windshear?. First there is a loud alarm ringing(in modern planes like the A330) + visual alarms (that wasn´t present at the AF, at least not this particular one), then you apply TOGA and pull the stick full backwards (check this video, is very well explained, also the part of the plane taking care of the stall in normal mode http://es-la.facebook.com/video/video.php?v=1015017491047010... ). The plane will flight just above the stall speed (in normal mode) and that way you´ll be able to avoid ground obstacles, as the windshear is only dangerous when flying close to the ground (take off, approach, and landing). If you have altitude enough you are able to change altitude for speed and recover the control without further problems.
Obviously the wind shear maneuver is not designed to be flown at cruise altitude, as the engines don´t have enough thrust to take the plane of the stall and keep climbing, also the plane is already very close to the coffin corner (over speed and stall aerodynamic limits are just a few knots apart), so any "extreme" maneuver (banking more than 20º or pulling or pushing hard in the controls) will simply put you outside of the flight envelope creating a control loss (usually you lose 2000´to 5000´ being unable to stop the descend), this happens also to planes entering sudden warmer zones like the ones you encounter in the tropic(due to the loss of air density).
There is a point when you simply disconnect from the alarms (no matter how many times stall or alternate law where sounding), you don´t hear them anymore (this was discovered or more studied with the Vietnam war pilots, who had very complex environments full of radio communications and SAM alerts), you only keep trying what you think will work, may it be the correct procedure, the incorrect one or just touching buttons because that damned computer is not behaving the way you want to.
Is difficult to know exactly how they suffered the problem and is also extremely difficult to judge it from a computer chair(even in simulator is well known the fact that the instructor can see obvious mistakes from the instructor chair, which the pilots are unable to recognize or detect for several minutes, once he sits in the pilot seat it is very provable that he will make similar mistakes).
What initially seem the correct actions(to the autopilot disconnection and lost of speed indication)are: to use the unreliable speed procedure(keep the throttle position and a pitch position) and then try to recover at least one of the speed indications (or at least checking which one was correct). But setting TOGA and then pulling the sidestick, this is (in my opinion) the automatic reaction to thinking they were suffering a wind shear(incorrectly), and so they keep fighting that imaginary wind shear for the long, long remaining 4 minutes till they crashed. No amount of other information or alarms took them away of that mental procedure (unfortunately), not because they where lost in they assumptions (they were), but because they thought almost all of the time (till it was too late) that they were performing the correct actions.
I must say that almost none of the pilots I know have the same opinion as me.(I am A320 pilot with B737 and MD80 experience).
