In the Air France flight 11 [0] situation the pilots thought they were having instrument and control issues, they had to go around, and there was much panic in the cockpit. It turned out the entire thing was pilot induced and the aircraft was fine. Because of Boeing's massive failures on the minds of everyone it'll be interesting to see if this was truly an instrumentation failure or something else.
If you read the final incident report[1] from BEA, you'll see that there was a hardware failure - the control yokes got desynchronised from one another which isn't supposed to happen, and the pilots were therefore unaware of conflicting inputs. Worst of all, Boeing doesn't warn in any way if that happens, because why would they? Airbuses (which don't have synchronised sticks) have "dual input" warnings audio and visual warnings.
They should have communicated better, but we've seen this many times - in panic situations or under pressure, communication is hard.
Ah, since I see the peanut gallery needs some education.
the control yokes got desynchronised from one another which isn't supposed to happen
No, that's precisely what's supposed to happen. Seriously. On an Airbus with sidesticks opposing inputs get you a dual input warning and have a button to lock out the other set of controls, and the computers just average the inputs. On a Boeing with yokes (e.g. the 777 in question) the way you overcome opposing inputs is simply to pull harder. Past a certain point (I want to say about 50 lb of force), the torque tube linking the controls "breaks" and the controls are desynchronized. If memory serves that means each pilot gets control of the elevator on one side.
Worst of all, Boeing doesn't warn in any way if that happens, because why would they?
This is also wildly inaccurate. The yokes are mechanically connected up until you apply enough force to break the connection. The feedback you get as a result serves as a warning. Airbus uses the aural and visual warnings because their sidesticks aren't backfed and you'd otherwise have no idea what the other pilot is doing.
There was no hardware failure. Air France simply trains their pilots to a very low standard compared to other airlines.
[0] https://simpleflying.com/air-france-boeing-777-serious-incid...