All this will probably come down to crew composition, very high workload, in adverse weather conditions, having to manually hand fly an aircraft which found it self in alternate law due to spurious information being fed to not only the flight display computers but also the flight control protection and guidance computers, simultaneously.
When something of this magnitude happens you are not only dealing with conflicting airspeed info, you are also presented with multiple spurious ecam warnings and cautions which is sometimes hard to ignore, also depending on the alternate law protection loss which itself can be further divided in two categories, or even direct law which would mean direct side stick to flight control input without any load protection leading to control overload.
Also when it comes to high speed protection, should this crew received wrong airspeed info indicating high speed situation, you have protection where once Mmo + few kts has been exceeded you will get an auto pitch up to try and maintain Mmo + few knots, so should this happen at slow actual airspeed, it will not be too hard to see why the pilot continued to pull back and continue increasing the pitch angle.
Direct law is there to give the pilot more direct control of the aircraft but it still has some protection to offer at the same time the protection on offer is only as good and accurate as the information provided to the computers involved.
Much more info is needed before one can create a picture on what went wrong when it comes to the decisions the pilots made in the last few minutes of the flight.
RIP all lost.