What I see more often is talking like their own public school system is fine, but that the whole thing in general is horrible.
I think it’s just the idea that something the government does could actually be good. They don’t notice or what to accept that the schools that underperform tend to have lower per-student funding, and that socializing the costs more would be the solution. If we pooled all the tax money for schools and then fairly handed it out to each school, things would be better. If private schools had to pay taxes to fund public institutions for the privilege of being to skip public schooling, that would get more funding.
Conservatives seem to me to believe that there is some sort of natural order where there are some people who are better than others, and deserve more. Exactly how those groups are divided changes—though the conservatives always consider themselves as part of the superior group.
That way, if conditions are bad for some people (who are not them) it can just be the natural order of things, rather than a problem that needs to be fixed. Such a belief lends itself well to lowercase-c conservatism, which is about preserving the status quo.