Is Bitcoin anonymous?

Bitcoin transaction's anonymity depends on public-private keys. The digital tie between a public and a private key is stronger than the tie between a person and his DNA.
If you committed a crime but the police had your DNA you would hardly consider yourself safe.
Furthermore there is a necessarily public list of transactions involving your public key and therefore connecting you to others by their public key.
To call this anonymous seems a stretch!

It is anonymous in that no one knows who owns the account unless you tell them.

They know you sent $100 on Tuesday. They know you received $700 on Wednesday.
They know exactly how much was sent and received by that account.

But unless you tell them who owns the private keys to that account, they know what the account did, but not who owns the account.
Unless you were mining at a legit registered mining pool that collected W2 info to pass onto your local government so they know how much you made and how to tax you for the past year.

There are other crypto coins that offer even more layers of protection and anonymous transactions by grouping several transactions together or by layering the paths like TOR does.