You are entirely too rational.
Conservatives generally have a running battle against all logic, knowledge and information, and are distrustful of education, anyway. Many would like to "privatize" all schools. The crackpot reactionaries--and that's who you're really talking about!--are primarily ignorant, uneducated, vicious psychopaths, who HATE education, knowledge of all kinds, anything sensible or rational, and ESPECIALLY loathe science. Many of them want to shut down anything remotely like real education, and replace it with a cross between concentration camps and Sunday schools, the better to orient the small, servile minds they cherish.
A lot of that is based upon the sort of misguided, distorted fake religion spewed by mercenary, predatory, profiteering businessmen like Pat Robertson and the late Oral Roberts, who call themselves "clergymen" but who are in fact pure promoters, in the most vulgar "show business" and "flim flam man" sense.
The ultra-right hates unions, and wants to outlaw all of them. Some of the scummier neo-Nazi types, such as the Koch brothers, ultimately would like to see the typical wages of the American working public reduced to about 1910 levels, and their taxes reduced to less than zero, such that the government, or what remains of it, would actually pay them just for being rich.
This is the warped scenario which underpins the entire "anti public school" movement.
What it really amounts to is book burning, in the old fashioned, right wing Nazi sense, without having to actually light the public fire.
The idea overall is to tighten up the control the oligarchic ultra-wealthy already exercise over the entire country.
What it would really do, of course, is launch a new dark age, and guarantee that the United States would cease entirely to exist within two generations, that place usurped by those wise enough to understand that neither technologies nor countries can advance without the best educations available.
Our K-12 schools have been behind Europe and Asia for over sixty years. Exchange students here to our high schools lose an entire academic year, which they must repeat when they go home. In some countries, a year here costs them two; the thinking is, being exposed to the kind of disinformation and lies they here in the more conservative venues is such that it actually contaminates the reservoir of overall knowledge. It's startling so few U.S. citizens are aware of a syllable of these facts, all well documented and long since proven.