Here are some typical answers(ranked in ascending order of corniness) I get from managers/bosses whenever I bring up the importance of having unit tests and code coverage as
One other thought to add to the other excellent comments on this thread (many of which I've upvoted): make sure that your management knows that Unit testing is very highly automated at this point. I find it very impressive to pop NUnit on the screen, hit the "Run All" button and see dozens of green-lighted tests being passed in seconds. Do that once, saying "this verifies that all of my older work is still correct despite all of my newer changes" and you just may win a few converts. In any event, they'll come to trust you - with your visible proof of quality - more than they trust others. That can only be good for your career.