These are two distinct jurisdictions of authority. The civil government has no authority under God for education, and is thereby usurping authority of the family in this regard. Because it is easier to defend ground you hold, than to fight to regain ground you've lost. We must maintain this ground. We must remain free of government tentacles of regulation.
Registration is the first step of regulation.
Because you must take a stand somewhere. Registration is the act which opens the door to everything else. If you don't keep the first domino from falling, you can't keep the others from falling, and once they have fallen, you can't put humpty dumpty together again. The place to draw the line is at the first domino. Resist all attempts at registration.