Germany, under Hitler, outlawed homeschooling, intent that the State, and only the State, be the educator of young minds. This is still the law in Germany (yes, Hitler's law is still on the books!) and it has just been upheld by the European Court of Human Rights, an arm of the anti-Christian, anti-Catholic "Eurpean Union".
For those who would like to know the Church's Teaching on this point, I refer them to The Charter of the Family, especially Article 5, Paragraph b, which states:
b) Parents have the right to freely choose schools or other means necessary (emphasis supplied) to educate their children in keeping with their convictions. Public authorities must ensure that public subsidies are so allocated that parents are truly free to exercise this right without incurring unjust burdens. Parents should not have to sustain, directly or indirectly, extra charges which would deny or unjustly limit the exercise of this freedom.
Of course, the last sentence speaks directly to the United States, where parents are taxed for the public schools whether they homeschool or send their children to Catholic schools, but at least they still have a choice, a choice now denied in Germany with the backing of the EU.