Suppose you are a member of a congregation who questions a specific doctrine but you don't want to commit to opposing it or signalling that you are unreliable? Suppose you are a member of the clergy questioning your faith, and not satisfied with the discussions you have had with people of higher rank within your religious order.
I think there is significant value in anonymous forums. For example the arguments during the drafting of the US Constitution probably would have been far less productive if they hadn't been preceded by anonymous and pseudo-anonymous discussions in the form of the Federalist Papers where proposals didn't carry the benefit of signalling allegiance to interest groups, or the disadvantage of signalling the opposite.
A great example today is the difference between the content on Quora compared to the content found on Hacker News. Just like a cover letter to a resume, a post on Quora may be truthful or interesting, but it is also inextricably linked to the poster's name and always suspect of being primarily interested in the effect it has on the poster's standing in the real world. Here, there are varying degrees of anonymity, and posts are more likely to be motivated by a sincere interest in exploring a topic or advocating an opinion, rather than what making such a statement says about the individual saying it.
For a real and current example, see the recent EFF vs. Watchtower case where a Reddit user /u/darkspilver posted to an ex-Jehovah's Witness subreddit. Watchtower subpoenaed Reddit for the user's IP address so they could excommunicate the user. If they'd communicated over Tor, this would be less of a problem.