I also work in aerospace software. Following DO178 certainly does not guarantee that there will be no software bugs. The point of DO178 is to follow a process that will _minimize_ the number of bugs by having adequate peer review processes throughout the requirement definition, coding, integration phases, in addition to the testing you mention above. Testing DO178 only tests that the code follows the requirements. If your requirements are fucked, so are you.
That is certainly one source for error. There are many. Another is that testing does not give you exhaustive coverage of the state space just because each branch of the code is visited.
The standard does mention "formal verification/methods/proof" but to my knowledge it's rarely been used extensively.
