It's not that it can't be done, it's just that sometimes it is nice to have a tool that helps you think about the code. Unit tested code isn't better in any way, it's just a style of writing code that can produce good quality code, but not the only coding style that can do that.
But I'd like to add that there have been quite a few refactors that I have done that would have been way harder if it hadn't been for the unit tests. It might not work for everyone, but I'd recommend you give it a serious try, it might be useful.
The tests don't just help you think about the code, they force you to do so. For those who are tempted to think "I can just do this quick change this one time; nothing will go wrong", tests force you to actually think.
Or they don't. If the tests just continue to work, then you ask yourself whether the change should have broken them. If not, you go on your way with a fair amount of confidence. But if the change should have broken the tests, then you have to look at why it didn't...
