Well, to be more precise, Bitcoin is anonymous. I don't know if it's pseudo-anonymity, but if you have bitcoins on an unmanaged wallet there's really no way for anyone to find out. Once you make a transaction, again, the same thing. But do you really care about your anonymity when using bitcoin? Many bitcoin enthusiasts just focus their money and efforts on making more money after investing. Anonymity is not their concern and neither am I. My biggest concern about bitcoin is its profit.
The way you acquired your bitcoins may well help the observer to determine that those are actually yours. Your "unmanaged" wallet must in some way interact with the bitcoin network to send and receive transactions, and a lot of information about your real identity is leaked upon such interactions. Moreover, when interacting with the network, you have to generate addresses that basically serve to represent you as a participant in the network. No matter how many identities you create, once you receive or send coins using one of your addresses it will be forever recorded on the blockchain, which means it can potentially lead to your real identity in case a piece of additional information becomes available or more sophisticated chain analysis practices are used. If you bought KYCed bitcoins on an exchange, it means you already attached your real identity to the address, so in this case, no additional investigation is needed.