Why is anonymity important?

Following up on these recent posts… here’s a twitter discussion from a couple of weeks ago…

F1000’s Caeser Berrios says that people who want to participate anonymously in post-publication peer review should get a senior scientist to relay their comments instead, and Matteo Malvezzi complains that anonymity makes it impossible to check for conflicts of interest. This might make sense if we were judging an ice skating competition, but shouldn’t scientific criticism be more objective and stand on its own merits?