Let's assume that someone had the capability to read your thoughts without your consent. An oppressive regime would thrive with this technology: Scan everyone's brain to detect undesirables to the state. Communications between members of a group are the organizations thoughts that they have not made public yet. Should a political regime have the ability to mind read that group? If no, you should support private communication.

Anonymous communications are the same thing. Pretty much all civil rights are born out of law breaking: A black and white person marrying, someone drinking beer (prohibition), people having homosexual sex. If all statements required an identity attached to them, no one would be able to anonymously campaign the merits of their ethical lawbreaking to advance social mores.