Why write unit tests?

This may be a dumb question but I'm a dumb guy. Where I work it's a very small shop so we don't use TDD or write any tests at all. We use a global logging trapper that prints a stack trace whenever there's an exception.

After seeing that we could use something like that, I don't understand why people would waste time writing unit tests when essentially you get the same feedback. Can someone elaborate on this more?