Well, personally, I'm an abolitionist. But even if I believed in public schools, there are many aspects of our school system that do not even make sense on their own terms:
1) Kids are mandated by law to attend school, but then when in school, teachers cannot even adequately punish unruly kids because that would violate their civil rights (thanks to a bunch of court decisions in the 70's). That means the worst kids get little discipline, and the good kids get locked in a building for six hours with juvenile tormentors.
2) Schools make less intelligent kids feel like they are inadequate because they are not as good at a narrow range of academic skills. And for what? There are many productive ways to earn a living that require neither algebra, physics, or history.
3) The worst delinquents do not want to be at school. The teachers do not want them at school. They do not get anything out of school because the teachers have no ability to control them. The system is benefiting no one.
4) Teacher pay has absolutely no relation to the quality of their teaching.
5) Districts pay a ton of money for the tools required to equip a vocational school. But those tools already exist in the workplace, and these craft businesses all used to except teenagers at entry level positions where they could learn the ropes for free ( or even get paid).
6) The smart kids who actually do want to learn are usually not allowed to. They are usually beyond the curriculum, yet are forced to go follow the exact curriculum set out by bureaucrats hundreds of miles away.
7) We live in an era where there is far more information in the world than anyone can ever learn, and where most economic value comes from specialization. There is simply no reason to have a centralized curriculum, outside of reading, writing and arithmetic.
8) There is no clear reason to have specialist teachers. Schools could be designed as parental coops. Or as a series of workplace internships. Or as apprenticeships. There are many, many models to use.
9) Why not use older students to teach younger students? It saves money and breeds responsibility.
10) Why segregate by age? Why cut off children from the rest of society in a big box building? Kids always act better when they are trying to impress someone older. Older kids act better when they know younger kids are looking up to them.
11) Despite a tremendous increase in the hours spent in school over the past 90 years, tests of numeracy and vocab among the general public have been flat.
12) Why assume that we need high school. We got through the 19th century just fine without it. What changed?
13) We send kids to college to supposedly educate them, but where the real result is spending 4 years of partying and no responsibilities.
14) The left puts up huge fights against voucher funding for private schools, because they fear that will lead to more class segregation. So instead, many posh suburbs have essentially become expensive private boarding schools where the parents live too. Instead of the different classes living in the same town but going to different schools, they live in entirely different towns altogether.
15) A student has his school paid for for 18 years. But after that he is entirely cut off. Why can't a student take a few years off when he's young and does not appreciate school, and then have the money available when he's older, and realizes he needs to a community college degree to achieve his chosen profession?
16) The school system pretends that it is supposed to raised up the lower classes and increase their earning potential. But in reality, the reason for much of the earning differential between drop outs and graduates is that there are needles barrier to entry laws for many professions. Take away those laws, and lower class students could simply self study and test into the jobs, rather than spending a huge amount on college.