Firstly you have to understand you cannot verify a system by testing it. You can never cover all the modes/events that could occur in practice. So testing only reduces risk rather than eliminate it. It is thus very important to design a system as thoroughly as possible to avoid faults rather than discover them in testing.
To test a system you need to know precisely what it is supposed to do, and then you need to know all things it will encounter. Humans are not good at these sorts of things. They like to take simplifications and elaborate them as necessary. Obviously there is a great temptation to stop elaborating when you think you've got far enough on your testing journey
Normally testing starts at a granular/component level since the overall system is the sum of its parts. You then test ever larger aggregations of functionality. However the best testing is that which tests the whole system at once. With aircraft that must include such factors as the people who fly and maintain the aircraft. the supply chain, the missions presented, varied weather conditions and so on. There may be just too many possible combinations to ever do this systematically so live line experience is the most reasonable way of picking representative test cases.
This is all of interest because the Boeing Max saga could be characterised as situations that nobody clearly foresaw. They didn't think through completely how an AOA sensor failure would create a challenging flightdeck workload. The individual effects would have been considered but perhaps not how they ganged up together against the pilots. Or Boeing may have actually realised this could happen and suppressed detailed investigation into how various levels of pilot skill might affect the safety outcome. Certainly the Max situation asks a lot of questions about testing