Simple fear of authoritarian government oppression. It was also decided in the very early days of our government that a national government bank wasn't constitutional.

With Snowden's revelations of things we mostly already knew, we can see that we don't really have much leverage over government abuse of power to collect and misuse data. The government is already doing broad data collections from private companies using secret courts... it would be a whole lot worse if the government already possessed the data.

With private banks, I can choose which one I use. There is at least some motivation for that bank to be on my side, and I don't have to wait for an election cycle and hope that my issue fits in with my side on other issues and that side gets >50% after 2 or 4 years ... my bank does something I don't like and I can switch today.

I don't trust my government to do a good job doing anything, or for anything my government does to not be vulnerable to political destruction (just look at the post office).