Reputation becomes important in pseudo-anonymous and de-anonymised sites. This often leads to popular individuals being able to take control of a discussion. Anonymous posting prevents one or two individuals from controlling discussion and acceptable viewpoints by sheer force of their reputations.

Anonymous posting lets people freely share ideas without threat of recpercussion.

Anonymous posting can allow the idea to stand on it's own, away from the name of the person.

Enforcing real name only policies could be akin to a form of censorship, limiting the freedom of users to post as they want.