"You are not attaching any form of ID to the transactions. Bitcoin is anonymous."
That is kind of like saying, "StackOverflow is anonymous. You do not attach any form of ID to your questions!" Of course, that worked out pretty badly for a certain high-profile Bitcoin user recently (yes, he leaked his real name at one point; however, he had also used his pseudonym in many other places, which was part of the problem):
https://medium.com/p/d48995e8eb5a
"by that logic nothing in the Universe is anonymous, since it's deterministic"
Hardly, in fact, all the evidence points to a probabilistic universe; by extension, probabilistic approaches to anonymity might be possible. It just so happens that in the context of electronic payments, that is entirely possible, and for more than 25 years cryptographers have been studying such things (and there is a pile of published research). Yes, you can even have an electronic payments system that protects your privacy from the NSA.