>Schools do not exhibit any of these characteristics.
This isn't a metaphor. Schools exhibit all of those characteristics. By your own definitions:
* People are placed there involuntarily.
Private and homeschooling is an edge case, but a red herring at that: it's nearly never the kid's choice as to which school they will go to, and (in some jurisdictions) they'll be hunted down and forcefully returned if they skip, in exceptional cases by men with guns. That's what "placed there involuntarily" means.
* Their freedom of movement is confined to the prison at all times (sometimes people serve prison on weekends, so I guess that's an edge case).
School rules generally prohibit leaving and punish violations with further confinement to the school if this rule is violated. High schools are slightly more relaxed about this but attendance is still enforced, in the more extreme cases by sending a man with a gun to apprehend you and return you to school. Again, exactly like a prison; the only reason students aren't locked in is because doing that would break fire codes.
* They are put there because they are criminals (or political prisoners, in the case of corrupt countries).
They are put there because, exactly like criminals and political prisoners, Society has decided that until a certain age they are not people and we can (mis)treat them however we wish. This isn't to make a judgment of whether or not this view is correct; but if you define "person" as a being that has the capacity to question and protest its station in life there are many "persons" held without cause in that underclass.
* They are intended as either punitive measure or because we decide society is not safe if certain people are allowed outside of prison.
We decided that the subsection of society that students comprise are not safe if they are allowed outside of school (and to the point that a lack of public schooling would affect literacy rates and the ability to participate in civil society, we're right).
Identical justifications are used to imprison political prisoners. "The purpose is not punitive, it's educational." is how their imprisonment and treatment are typically justified, too.