Tests in software development bring great value, but the reasoning behind why tests are of any good is usually rotten.

Coverage and regression handling?—Well, yes, maybe 10% of the total value.

Test-driven development eases writing code?—Indeed, another 30% of the total.

And welcome the winner. 60% of the total goodness brought by tests is that by writing tests you understand how good is your new API. And yes, everything you test is indeed your API. Nobody should test privates.