Why are automated tests worth the trouble?

Imagine a factory line that has a machine putting holes in sheets of steel. These holes have to be of specific size and shape so that they can house bolts that will hold the finished product together. The designer of such a factory line will set up the machine, test if the holes are correct, and move on. Sooner or later, something will change: the factory will use different, thicker steel; a worker will accidentally change the hole size; or, simply, more holes need to be punched and the machine has to be upgraded. A smart designer will put quality-control checks at certain points on the line to make sure that the product follows the specification and retains its key qualities. Holes have to conform to particular requirements but it doesn't really matter how they are created: drilled, punched, or laser-cut.

The same approach finds application in software development: it's very hard to predict which pieces of code will remain unchanged...