When I’m working on a piece of writing, like a story or a novel or sometimes even a blog post (not this one), I write it by hand. Like, with a pen and a piece of paper. I, too, was amazed that such things still existed.
I don’t really know why, I just find it easier. Easier to compose, easier to get all my thoughts down before they escape from me. Easier to flip back and forth between things, draw little arrows and things to indicate where I should move text, scribble things out furiously when I don’t like them (but still be able to see what I wrote in case I need to mine a badly written passage for small gems). Easier to carry around a notepad with me than a laptop. Easier to not be distracted by Freecell and the Interwebs constantly.
In fact, I have found there to be only one downside to this method of writing, for me.
Once I’ve written something, I still have to type it up.