Who is to judge her ability to homeschool? The state!? Who granted the state the authority to determine if Mrs. O'Dell has the ability to homeschool her own children? Where did that power come from?
Let's review - maybe it will sink in this time:
The legitimate powers and authority of the state are delegated to the state by the people. Therefore, all powers and authority assumed by the state that were not explicitly delegated to it by the people are illegitimate. Illegitimate power is another way of saying tyranny.
Now, in order for the people to delegate a power or authority to the state the people must first possess that power or authority. Our Republic is founded upon the principle of individual, inalienable rights granted to each person by his Creator. From those rights an individual derives certain powers and authority over himself, his family, and his property. For example, the inalienable right to be free grants the individual the right to protect his freedom. The inalienable right to enjoy the fruits of his own labor grants the individual the power to protect his property and to hold authority over it. The inalienable right to life grants the individual the power to protect his life.
This individual power and authority extends only to one's self or to one's family. And individual does not legitimately possess the power or authority over someone else, their property, or their family. For example, if you had a neighbor whom you felt was an inadequate home educator you do not possess the legitimate power or authority to take that neighbor's children away and educate them differently.
If an individual does not possess a certain power or authority, they cannot delegate that power to the state. Again, if you individually do not possess the legitimate power or authority to take an errant neighbor's homeschooled children away you cannot delegate that power to the state.
So, I ask again, where did the state get the power that you so readily endorse? Where did they get the authority to determine if Mrs. O'Dell has the ability to home educate her children? Where did they get the power to remove the children if they made the determination that she couldn't? If they state did not always possess that power, at what point did they assume that power? How was it possible for them to assume that power? And, to pre-empt one of your obvious arguments, what political philosophy or idealogy holds that the needs of the state or of the society outweigh the rights of the individual?