The top reason is indeed Knowing Your Code Works.

Be it because requirements keep changing, new features are added, many people working on the same code, refactoring, whatever... Having good unit and functional tests catch a huge amount of problems that would be hard to find latter.

The other two points are pretty minor in my view.

And the suggestion to improve code coverage is just cheating. There's no excuse for that. Either don't track stupid metrics, don't add unnecessary catches, or properly test exception code.

EDIT: Clarified text.