This is a big question. The short answer is: The workload of being the publisher too is the biggest challenge.
You have to write and edit your story, just like any writer does, but then you also have to typeset it, manage files and file formats, come up with cover art and title font (while respecting other people's copyrights), optimize that art and font for display on various screens, get the files up and looking decent on a variety of different publishing sites, then market the book in a saturated, often-hostile-to-self-published-books environment.
You have to do everything a writer does, then everything a publisher does. It's a lot of work.
It can be extremely satisfying to be in control of everything, for people with the temperament and energy levels to do that, especially if you see it pay off in the form of sales. For other people, however, it steals too much time away from the writing part of the process.