Homeschooling terrifies the Left because the Left is at its core totalitarian, seeking to bring political discipline to every aspect of life — and control of education is essential to that project. The public school is in miniature what the Left believes the world should look like: Everybody arranged in orderly rows and moving about on an orderly schedule punctuated by bells, being taught about diversity and climate change by nice union ladies who also lead them to their federally subsidized lunches. If you can say “no” to that, you can say no to any part of the Left’s vision. Homeschooling is an existential threat to the privileged position of the institutional Left. The schools are the factory in which it manufactures its future clients.
Of course it doesn’t help that homeschooling is associated in the public mind with a particular strain of evangelical Christianity, as in the case of the Romeike family. It is distasteful, but it should not be a surprise that the Obama administration has no objection to the political and religious suppression of such unruly Christians — the Obama administration is doing the same thing to the Little Sisters of the Poor and other Christian groups that it finds inconvenient.
In the case of the Romeike family, a judge already had seen fit to offer them asylum, but the Obama administration wants to hand them over to the Germans.