Your tests are probing your code on a narrow range of inputs (or if you're using something like property testing, potentially a larger but still finite range) drawn from the valid state space that is almost always too large to actually verify. They're also themselves pieces of code that itself can have bugs. Formal methods can prove properties about code, but usually w/ a much larger investment of time.
> The need for a debugger is a symptom of a sick system. I have never required a debugger on a healthy system.
I think people who say stuff like this are probably a little in denial about how many bugs they've actually written and how difficult it is to get any kind of certainty about the correctness of their code. Programmers write bugs, why are we policing the tools they use to fix them?