If you choose to become a self published author, distributing your own books via print on demand or other self-publishing service, there are some good reasons why you might choose to write under a pseudonym. Obviously writing under a pseudonym is not the path to personal notoriety and fame. For the following three reasons, though, it makes sense for many self-published authors to write under a pseudonym.
Pseudonym reason number one: freedom of expression. Writing under a pseudonym is liberating. If you can be certain that no one will figure out who you are when you write then you will feel much more free to write whatever you feel like writing. For example, as an employee in a corporation you might be very hesitant to write a book about dealing with difficult coworkers, knowing that your coworkers are likely to find out that you have written such a book; in that situation your coworkers would inevitably believe that they are the difficult coworkers you’re writing about. If you can write under a pseudonym, though, you will likely have no hesitation to write that type of book. Writing under a pseudonym also might make you feel more free to write about personal medical conditions that you have experienced and other issues that you would not want attached to your name.
Pseudonym reason number two: prevention of future embarrassment. In the Internet age everything we write, whether it is on the web or in book form, follows us for the indefinite future. Sometime in the future you will interview for a job and your employer will do a quick Google search to see if there is anything strange in your past. By writing your self published books under a pseudonym you reduce the chances that a future employer will find something that would disqualify you from working for the employer. For example, imagine that you write a book criticizing global warming as being a massive, conspiratorial scam; then, years later, you have a change of heart and become an advocate of fighting global warming. You seek a position with an organization that lobbies for anti-global-warming legilsation. In that situation you would not want the organization to discover your earlier writings. As long as you wrote them under a pseudonym, that would probably not be a problem.
Pseudonym reason number three: branding an author name. I suspect there are very few authors who are interested in only one type of book. For example, Agatha Christie wrote dozens and dozens of mystery novels, but I bet she read her fair share of science fiction and romances, as well. She might even have been interested in writing a science fiction or romance novel, but her name was so tightly associated with mystery novels that she could not realistically have done that. Very few authors are able to succeed in multiple genres, partly because they become pigeonholed into the genre that makes them successful. If you write under a pseudonym, though, you can enter as many genres as you like. You could develop different brands by using different pseudonyms. For example, John Smith could be the name you use when you write science fiction books, while Albert Jones is the name that you use to write horror suspense novels. Using pseudonyms in this way will avoid confusion by readers when you choose to write in a new or different genre.
These are three of the top reasons why self published authors write under a pseudonym. There are undoubtedly many more. For centuries authors have chosen to write under pseudonyms and that practice is likely to continue for the indefinite future.