Fear. We’re afraid of government-run medical care, but government-run schools aren’t that scary.
When we think of government-run programs, we generally think of standing in long lines at the DMV (or TSA groping lines) dealing with surly and unprofessional government workers, senseless regulations, having to fill out redundant forms in triplicate, long waiting lists and inconvenient scheduling, bureaucratic ineptitude, etc. Generations raised during the Cold War were led to believe that everything was like that (only worse) in socialist countries. We don’t want that in our health care because health care is important to us, immediate, and a life-or-death matter.
Schools, on the other hand, are mostly just babysitting centers where we can send our kids while we work. They serve a useful function of keeping our kids occupied and hopefully fairly safe. They’re supposed to provide education as well, but that’s not immediate and it’s not a life-or-death matter. If they’re inefficient, unpleasant, or filled with bumbling bureaucrats, that might annoy us, but it’s not such a big deal. If our kids have to wait in line and fill out repetitive forms to be taught something, so what? The smart ones will have learned it on their own already anyway.
There’s a big difference between a school accidentally teaching a kid geometry instead of algebra, and a hospital accidentally doing a heart transplant instead of a lung transplant. People are afraid of dying while waiting in line for medical treatment, or being unable to get necessary treatment due to red tape.