This is partially true, but this (and other replies) are all somewhat wrong/light on actual information. You're correct in saying that Tor assures anonymity an

This is partially true, but this (and other replies) are all somewhat wrong/light on actual information. You're correct in saying that Tor assures anonymity and not privacy: if you don't want other people to know what you're sending over Tor, it needs to be encrypted separately, because the communication between the Tor exit node you're using and the computer you're communicating with is unencrypted. However, Tor still relies on encryption in order to provide anonymity, and messages are still encrypted when you first send them out (whether or not you're running a Tor router yourself). Tor does onion encryption: when you send out a message, that message is wrapped in three layers of encryption. The first router you send it through can take off the outer layer to see who it send it to next, the second router you send it through can take off the second layer, and the third (exit) router you send it through can take off the final layer of encryption and see the actual message you sent (and where you want it sent). This encryption is very important, because it assures that each router can only see its immediate neighbors in the chain. If the encryption is broken, then whoever breaks it can see the entire circuit the message is traveling along (which will include the source and destination) and so anonymity is compromised.