Metadata. An adversary can determine which parties you are communicating with. Although those parties may also be anonymous, metadata in aggregate can sometimes tell a story. If an adversary can determine who you are communicating with and look at their accounts, he may be able to find unencrypted messages. Track down enough parties, read enough accounts, and he can infer things about you. It's less secure than an "everyone gets everything" system like BitMessage, where an adversary can't prove which messages were sent to you. Well, that would be the case if it were true: https://bitmessage.org/forum/index.php/topic,1666.0.html