I think its because both need to house a large amount of individuals in as small a space as acceptable to the outside society. But also, both are ultimately mechanisms of authority that shirk their supposed goals of education and restitution/rehabilitation.

Related, perhaps unpopular opinion: It's outright silly how we expect a good learning environment to come out of putting all of our socially unformed minds into one big facility, with little behavioral supervision (10-to-1, 15-to-1, or worse), and compel them to move from location to location by a bell, and to perform rote memorization in order to meet some metric of success. It's sillier how we expect children to come out of this environment socially well-adjusted, having learned something of value, without psychological trauma, besides the experience of navigating a system of hierarchical authority. You know the wisdom passed down by my liberal (using liberal here in a very strict sense -- NOT necessarily left leaning) Catholic father, who ostensibly would defend the value of educating the public (though, perhaps not the value of public education)?

"Find out what the teacher wants and give it to them."