The very first article in the NH Constitution reads “All men are born equally free and independent; therefore all government of right originates from the people, is founded in consent, and instituted for the general good.”
In a free society, government is supposed to be accountable to the people, not the other way around. Testing within the public school system is legitimate since it is a mechanism for making sure the money taxpayers have spent has shown results. It’s a way to make the schools accountable to the people. But no taxpayer money is spent on a homeschool program. In fact homeschoolers pay taxes for schools they don’t use, despite the fact that they generally give up one income. "Home education" regulations perversely forces these families to become accountable to the government.
The legislature of N.H. is constitutionally obligated to govern by consent. There are many parents in the homeschooling community, including myself, that are not willing to consent to regulation of our ability to educate our children at home.