Writing unit test and moreover having them in place when developing is a great thing. They give you some kind of assurance (if well done). I mean, you can modify things without fearing to break existing code. Afterwards you just run your tests and check if everything is still fine. Of course this does just hold if tests are written properly and you have a quite large test coverage.But explaining people which did never work with unit tests nor even heard of them at all is extremely difficult. I mean, it's clear. Why should I code more, "waste" more time to reach the same goal? As I said, it's difficult and in such situation don't even start talking about test-driven development or the less used name test-driven-design.
But if you're interested in reading something about it, here's a blog post on the great Google Testing Blog, which describes a nice analogy between building software and a car. And it really highlights very nicely the advantage of adopting test-first strategies versus test-last.