Tenth Amendment: The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
Seems pretty clear to me. There is nothing in the Constitution that gives the federal government any power at all to regulate education in any manner. Since such power is not specifically delegated to the federal government, it does not exist.
I would argue that as a matter of sound public policy, the power to regulate education ought not exist at the State level either. But I would not argue specifically that they are constitutionally prevented from doing so. That legitimacy of such an argument would have to depend on the specific language in the individual state constitutions.
But clearly, education is not a Constitutionally authorized federal function. Tell me. Why do you think it is (or might be)?
And "raise"? What does that word really mean? Bet you thought it meant to just go out and recruit - and that would be your thought!
Somebody else could view it carrying with it the same sort of meaning that we would have in the phrases "raise a garden", "raise a child", and so forth. With our Constitution recognizing that ALL of us are going to end up in the militia, it seems pretty clear that the very same Constitution empowered Congress to "raise" us up for that eventuality.
Now you go along and read the Constitution your way, and I'll read it my way, and my army will kick your army's butt!