As you are using this phrase in a context where I feel like you are bringing up reasons for Bitcoin, I feel the need to clarify: cash is private (only two people can see any transaction: the two people transacting), classic banks and credit cards are less private (three people can see your transaction: the two people transacting, and the bank), while Bitcoin is the opposite of private (literally everyone is required to see your transaction, whether or not they particularly care ;P).

You can try to hide your transaction by handing it to a mixer, but then the mixer is serving the purpose of a bank and is "fighting the current" by trying to pretend to offer a private service when their actions are also recorded in a public ledger, which means both that mathematicians might later find mistakes in timing that allow them to deanonymize your mixed transaction but also that small mixers are worse at this while larger more centralized mixers are more useful... the exact opposite property for what you want if you really didn't like the concept of a bank managing transactions.

And no matter what solution you come up with, fundamentally the transaction requires at least one other person to know that you are sending money as you need to use a public network to try to communicate with someone to tell them to tell others to eventually move the money by adding it to a mined block. The only way Bitcoin can even try to simulate the real and true privacy of cash is if you meet someone in person and hand them directly a slip of paper with the private key of some money on it... but then they have no way to know you don't have a copy, at which point they have to announce to the world they received the money in order to re-secure it with their own key.