The "danger" is not to students, but to the established order that governs what they learn. Maybe the practice is not universal, but I was shocked to learn that in some schools which follow government curriculum "guidelines", algebra and geometry are not taught until the student is about 16 years old. That may not be coincidental.
In pre-history when I was a kid, I clearly recall being introduced to algebra when I was 9, and think that I had already been shown by then the key properties of triangles. So there's a seven year difference, between what was taught then in England, and what is taught now in America. How come?
Here's a possible reason: above all other subjects, mathematics trains the young mind in reasoning ability. Given A, prove that B or deduce the value of C. Geometry particularly presents the student with a premise, and invites him or her to figure out a conclusion. And that conclusion will be discovered to be accurate and unique; the proof, once developed, is absolute. So to every math puzzle there is one answer and it is found by logic. Opinions and shades of gray do not play any part; nor, of course, does dogma.
Rust has grown deep on my mathematical skills, so when I encountered the following recently it took me far too long to see how to solve it. Try it for yourself:
√(x+15) + √x = 15
That is, the square root of (x+15), plus the square root of x, equals 15; solve the equation for x.
I found the answer (x = 49) in about five minutes by cheating; I tried the 8 possible combinations of integers that add up to 15, to see which pair fits. But that's not the way; the question does not say the answer must be an integer, nor that it is unique; and in any case failing to discover an algebraic sequence of steps to solve the problem spoils the fun.
Eventually the answer came to me in the wee small hours (I prefer that to counting sheep) and half a dozen steps of elegant reasoning produces the absolute proof that x is certainly and exactly 49, and only 49.
How very different is all this from the way government likes us to think! It has no need for us to reason things out; it requires only that we obey. School is not for training youngsters how to think, but for teaching them what to think. So it is for all government schools and even for for-profit schools that follow government guidance - which means, pretty well all. So is the population dumbed down, made submissive, by successive doses of this treatment over 7 generations.
Mathematics is the tricky bit, for those government indoctrinators, for the very essence of math has to do with reason - mankind's primary distinguishing attribute; and since math cannot be wholly omitted from the curriculum it is postponed to an age by when a great deal of the indoctrination has already taken place. Meanwhile the victims are forced to pay for this destruction of their own intellectual ability, while the indoctrinators take credit for making sure even the poor receive a "good education." Y-u-c-k.
Though math is king in my opinion, there are some other subjects which, if taught, risk bringing the institution of government into ridicule or distrust. Traditionally schooling had to consist at least of the "Three Rs" and the first two are Reading and wRiting.
Reading, government indoctrinators can handle fairly easily; they just snow the student with a list of books that have been well vetted as suitable for a statist environment. The Scarlet Letter, to help undermine the idea that there is some source of independent morality other than the relativist version they promote; The Grapes of Wrath, to impress the child with the risks of independent farming and the need for Auntie to care for us all, and so on. George Orwell and Ayn Rand threw rocks into that smooth stream of indoctrination, but very cleverly even those works have been incorporated along with a narrative about what they "really" mean.
Writing has been shattered. In my schooldays we were positively encouraged to write essays, on all manner of subjects, and to structure them well and by all means represent a viewpoint. They were judged on how well the writing presented the case and persuaded. Today even the basic building-block of cursive handwriting has been scrapped, and the importance of correct spelling and grammar discounted; as can be confirmed by glancing at a string of comments on any public Internet forum. Coherent arguments are rare. What need, after all, have government-school graduates to express an independent view? Uncle will tell us all what to believe.
Close behind the 3Rs comes History, which has been very widely replaced by such vital subjects as sociology and feminism. History presented the indoctrinators with the problem that in any account of the actions of any government, each student can look at the facts and form a judgment about how well it performed; and facts about the effects of various policies can be brought in to support such analyses. That can be highly dangerous to promoters of the Doctrine of the Infallible State. Much better to focus on present-tense behavior, whose ultimate results lie in the future and so cannot be evaluated. Factual history presents abundant evidence of the utter, destructive folly of government policies all over the world, and a study of them might very well suggest to the student's mind that mankind would do much better without any. No wonder the curriculum moves the subject aside.
The urgent need is to remove government control of the curriculum, and such is the multi fanged grip it has fashioned over that in the last century and two thirds, I see no hope of that happening, short of the total elimination of government. Nothing less will do.