Exactly, paying with a credit card is more anonymous than paying with Bitcoin. With the former, only the CC company, the merchant, and presumably the government can see what you purchased. With Bitcoin, anyone with a blockchain explorer can see your when and how much you transacted.
That's a bit inaccurate, your identify isn't attached toe the Bitcoin public ledger. It also has to be inferred through 3rd parties such as your wallet or some BTC exchange.
While bitcoin can be anonymous (buy with cash, use a mixing service, change your bitcoin address every time, only pay over tor/i2p), they aren't made for that. Also keep in mind that every transaction is public, even if it can't be traced back to you.
? You're confusing security with anonymity. The bitcoin mining strategy ensures that transactions are secure, untampered (ID theft? counterfeit bills? credit hijacking?), thus securing anonymity if it is developed (throw away accounts, as said above) when and where needed.
The problem with classical currency is that anyone can spoof anyone else and the system inherently cannot prevent this. Fraud correction is a painstaking manual/organic process involving customer service, account IDs, and headache.
You can build anonymity on top of it by using throw away accounts, but it's not an inherent part of the system.