[NDT]

Anonymity comes from not knowing someone's bitcoin address which in many cases is safe to assume.

[beagle3]

It is never safe to assume, because it could be (retroactively) revealed at any point in the future. The right term for this is pseudonymity[0], not anonymity.

[0] https://en.wikipedia.org/wiki/Pseudonymity

[devdoomari]

but... how?

suppose money went from A-->B-->C-->D-->E, and B,C,D never uses an bitcoin exchange / other 'offline' purchase / etc. (Also, B could send to C1, C2, C3 and then so on to hide the track.)

then, how can anyone be sure that A,B,C,D are the same person/different person?

Or... by "retroactively" - do you mean sometime in the future (hopefully far far away) where bitcoin's hash algo. is broken?

[georgyo]

Or the simpler answers, something on your computer reveals it, like malware.

Or the person who sent/received money to/from you revels who you are, or information which helps identify who you are.

Or there are warents authorizing authorities to take your devices and then they have all your identies.

Also when you send Bitcoin from a wallet that has received money to multiple addresses, you can't be sure which coins are being sent. As such they can also associate multiple addresses together by which coins they sent.

[qiqitori]

By design, every single transaction is tracked. Otherwise you'd have a hard time proving that you have any BTC at all. In fact, the miners implicitly verify that all purchases are tracked, by doing something like the following every "block":

new_hash = hash(previous_hash . all_new_transactions . random_number)

You won't immediately know if A, B, C, and D are all the same person, but you can look at what has happened at those addresses (or previous addresses) in the past, and (eventually) what happens in the future, and draw conclusions from that. If you use a new address for every transaction, and never merge your money, you may be able to obfuscate the flow for a while, but you have to make sure you don't leave any patterns in the timestamps, and make sure you generally know what you're doing. Any mistake could mean that people know it's you. Moreover, money is generally used for 'offline' things eventually. You may purchase something from a completely normal person who doesn't obfuscate his transfers at all, and then get outed when the police ask that guy who they got those suspicious coins from.