A world where all code was written and the frozen, and all extra features were just built entirely 'above' that code would mean that all you needed to do was manually test the code you added, confirm it works in each path of logic and be really very sure that it was correct. However, this world is a) not a pleasant dev world and b) not a realistic one. Code always needs to be altered, extended or improved. That's a given.

Let's suppose its you that's changing something existing. You change something. Did you break all the other stuff that relied on that? Probably. Tests are the only remedy. Change some code, improve an algorithm in the backend, adjust the way a process happens in a frontend, rewrite a database query to be more efficient. If you have tests you're safe, and you feel safe. Boss tells you a client is trying out that code, you feel confident, there's no fear of the unknown things you never considered. Look at your spec, look at your tests -- they should be fairly easy to match up. System needs to be able to do something? Ok, lets write the test for that. Even if a bug does get reported, write a test that fails, code the fix until the test passes, ship it. Then just be confident. Your tests give you the armour of confidence.

I thought of the analogy of armour based on my -- sadly ongoing -- dual life doing dev as well as support. In a support role, your armour comes from confidence in your knowledge of what you will be asked questions about, or what to do even if you don't know. Your course is clear and you have your armour of knowledge. Shipping code that isn't tested feels a lot like answering the phone to someone who you know is going to ask you something you don't know anything about and you don't know where to turn. Don't be so foolhardy as to go without such a vital comfort, for the sake of, if nothing else, sanity.