I think why some people call is private currency is because it has not been accepted globally by central bank . To us investors, users and traders of bitcoin it is not a private currency.
Bitcoin is a public currency hence there is no doubt.We should all see bitcoin as an amazing another currency which is capable of being used as currency for all business transactions.
If you will just be doing a Google Research for Private Currency, you can know why.
First off,
private money is a currency issued by a private entity, be it an individual, a commercial business, a nonprofit or decentralized common enterprise. Bitcoin is a crypto currency, hence it is a private currency since it is issued or developed by none other than Satoshi Nakamoto, the "private entity". It is also said that it is contrasted with the fiat currencies that is issued by the governments or central banks and Bitcoin is.