I think it is wrong to call bitcoin a "private" currency.
On the contrary, imo bitcoin is much more of a public currency that any national currency is.
I think bitcoin can classified as "private currency" because if you have bitcoin no one can trace that you have it even government cannot determine who are the people who have bitcoin. Yes, bitcoin knew in many countries but no one can know who are the people who have it. So that I conclude that bitcoin is a private currency.