You could say Bitcoin is pseudonymous rather than anonymous. The key difference is that with Bitcoin, you start with a new, random identity each time you create a new address. If you use a new address for each transaction, there’s nothing tying them together.
The challenge is that if any of the addresses in a group of transactions can be identified as belonging to you, the others may also be identified as yours. The risk is that if you use addresses that have been connected to your identity, the corresponding transaction history could potentially be traced.