I disagree. Competency to teach is different from the protected "right" to procreation.
After all, any one with sperm, eggs, and a womb can create a child.
You misread what I said....competency to teach one's own child, not teach others. We were talking about home schooling.
I wonder, is the right to procreate the same as the right to be a parent?
Competency to reach ones own child what?
Education as we are discussing it requires knowledge that may be beyond most parents. That isn't to say it can't be accomplished or obtained, it does address the fact that many parents have no grasp of many subject sufficient to instruct in it. Nor do many have the time or real desire to obtain that basic mastery.
Which is why we employ specialists. It's more cost effective to fix the system rather than spend time and other resources reinventing the wheel for x number of home-schoolers.
As to parenting rights, settled law would have that as yes. If you open the right to be a parent as a licensed thing you really have a mess. Everything from abortion to discipline, to education.
License parenting and you have the first step to a Brave New World. I refr to the novel. That is a receipt for Big Brother style government.