I know from experience that when I write code without unit tests, I'll get a few issues that come up to fix, but when I've written the unit tests I rarely hear of issues. Also, from time spent writing unit tests I write better code to begin with. I look at methods and think of the ways they could fail and build them from the start not to fail or at least to fail in a better way.
Unit tests ARE essential to writing better code, but it also will make you a better developer because you SEE areas where things could go wrong and fix them before you ever get to testing.