Because you don't engage manually any more. As I pointed out in above, the A (air superiority) version has only 120 rounds of ammo, which is three seconds worth.
If you're using the gun you tell the computer "I want to shoot that guy", at which point you try to get him onto the pip on your display, which is going to move around depending on your relative velocity and distance. The computer actually fires the gun when it decides the round will hit. If you had to do it manually you'd most likely run out of ammo before you hit anything.
The air-to-ground system is similar.
So the software isn't just firing the gun. It's integrating data from all its sensors to figure out when to fire based on what you're trying to hit. I assume they have cut-outs friendlies as well, so you don't accidentally shoot your wingman.
My incredulity is not because I think it's easy to write reliable software, but because a cannon shouldn't need more than "if button then fire." From the other reply, apparently it's way more complex than that though.
Additional complexity comes from the F-35's Stores Management System (SMS). In addition to the basic accounting tasks of keeping track of what kinds of weapons are loaded, and on which stations, the SMS keeps track of how much the stores at each station weigh and provides that information to the flight control system (FLCS). FLCS can then compensate for the weight distribution of the stores. The gun must integrate with the SMS.
If you're using the gun you tell the computer "I want to shoot that guy", at which point you try to get him onto the pip on your display, which is going to move around depending on your relative velocity and distance. The computer actually fires the gun when it decides the round will hit. If you had to do it manually you'd most likely run out of ammo before you hit anything.
The air-to-ground system is similar.
So the software isn't just firing the gun. It's integrating data from all its sensors to figure out when to fire based on what you're trying to hit. I assume they have cut-outs friendlies as well, so you don't accidentally shoot your wingman.