A prison is a place where people are deprived of liberties. A society can justify depriving people of liberties. A private interest should not have the right to do so.

Yes, it's not the private interest who condemns the prisoner, but they run these facilities at a profit, turning what should be a rehabilitating environment into an environment that is designed to promote full prisons to enrich an individual.

A good prison should work at a financial loss because there should be a societal benefit to rehabilitating inmates. If a higher prison population turns into a financial incentive, there is no incentive to help inmates or even reduce recidivism.

This is especially true when you consider how many minor offenses can send people to jail in the US. It is also interesting to consider that when slavery was abolished, many plantations turned into for-profit prisons; or that the incarceration rate of the US is the highest in the world.