Most if not all message board software do not allow this option as it can cause both issues with the database that displays the information and also would allow spammer and hackers to sign up, make their spam or hacking posts, then delete their account leaving no trace of where the post came from. This is a safety issue for any site that operates a message board.
One of the easiest ways to not participate on a message board is simply to not log in and make any posts.