Well-tested code provides peace of mind to the developer. If you get a feeling that writing a test for the new method you are developing is too much of an overhead, then you usually don't get it right the first time. You have to test your method anyway, and it is less time-consuming in the long run to set up or write a unit test than to build and start up the application many times—every time the code changes and for every logical pass through.
One of the reasons we often feel pressed for time is that we do not include in our estimates the time needed for writing the test. One reason is that we sometimes just forget to do it. Another reason is that we shy away from giving a higher estimate because we do not want to be perceived as not skilled enough. Whatever the reason, it happens. Only after years of experience, we learn to include tests in our estimates...