I think you have some very good concerns that need to be explored. They are most certainly areas in which there is great agreement and a few that I would add some thinking.
My concerns/objections are (but not limited to:smilewinkgrin

:
1)children are being asked to be missionaries when they themselves are not yet regenerate.
Perhaps a better word I could have used was witnesses. There are no family secrets especially in the public school. What happens at home is shared at the school. That is the nature of small children. They have no boundary of shame or thoughts of what is inappropriate (not speaking of older children). So, as the home talks of the wonders of God, the child will witness of those things at school. Regenerate or not the witness takes place.
2)they aren't given adequate time to mature- physically, mentally, and emotionally- before being sent into a situation as unsupervised and challenging as public school
It is very good that parents be highly aware of all aspects of the child's growth. Unlike many dysfunctional family situations, the believer's family should be structured on the principles of the Scriptures. Personally, I think the greatest hindrance of the modern education is the age/grade system. I have seen six year old children able to work two or three academic years ahead, and those who were older unable to read. All aspects need to be considered and factored into any educational setting and a wise parent will moderate that setting accordingly.
3)that Scripture never gives us any reason to believe that children are to be 'sent' unsupervised into any kind of 'mission field'
I agree. If the school (public, private, home) is "unsupervised" there is no accountability.
4)parents aren't given the authority or directives to 'send' their children on any kind of spiritual mission
I agree. Yet, we send them off on all kinds of occasions - summer camps, overnight stays, ...
The point being, that wise parenting stresses discernment. Even the home is a spiritual mission, perhaps the greatest mission field, for it is where the foundational truths are taught. It is also where the Satan is most active!
5)the Biblical pattern for missions is to go out in twos- are children sent to school with a spiritual partner? I think not.
I would be a bit careful of putting great weight upon the "two" and put more upon the fact that "I am with you, always..."
I say this because, even now in the national news, there is a young teen lady who will probably end up in a foreign land where she has no language skills and no background. Her immediate family died and the next of kin are illegally here from Brazil.
For parents to assume they will always be there for the children (especially in the uncertainty of the age) may be good for the child, and that is right to say. But, better is that Jesus will never leave them.
6)parents are instructed to educate and admonish their children in Scriptures, and we are forbidden to tolerate false teaching and false teachers in our midst- and somehow a public school education doesn't qualify?
I agree that parents are the final authority - although all states have laws making them the final authority by virtue of the right to remove, without court order, children from the home. I think that is horrible law! Necessary, but still horrible.
However, I would caution that you don't apply the false teaching aspect (for that is for the assembly and the false teaching of Scriptures) to the typical school (home, private, public). Teaching evolution isn't false teaching as much as it is presenting commonly heard thinking that needs to be continually inspected and refuted in the home.
We taught our children that they have the right to respond to a test question with the answer the teacher determined was correct, and then to inform the teacher of why they rejected the answer. That way, they satisfied the requirements and still stood upon the principles of faith.
7)that after an 8-hour school day and the typical 2-3 hours spent on homework, exactly how much discipling and admonishing does the average parent have time to do with their child in the evenings? They spend what time they do have deprogramming their kids instead of teaching and bonding with them. The way some of my public school friends live sounds more like the school has custody and the parents have visitation rights on weekends.
I remember the same argument being expressed by those who sent their children off to "Christian" colleges (Baylor, Stetson, Howard Payne...) and then found their children "rejecting the faith."
Would that the parents had taught their child discernment!!!
The problem isn't "programing" the child, for such programing doesn't last in the hormonally driven days of "my parents are dumb."
In my opinion, there are two times a parent can significantly mold the character of a child. Ages zero to three - they learn that "no" means "no" and the ages 10 to 13 - they learn "no" still means "no."
Certainly, some parents have abdicated the throne to others. Would that parenting skills were innately found in all adults.
8)criticisms like this (not fulfilling the Great Commission) are often aimed at homeschooling parents, but not at those who send their kids to Christian school. Why not?
A most excellent point!!!!
During the 70's and 80's a lot of churches jumped into the private school industry, and the thinking was to "protect the children" and "raise up an army for the Lord." Some also put political, educational, racial, social and other agenda's into the mix.
The question is similar as you asked. Where is the army???
Again, it came down to parents abdicating to someone else the responsibility.
Here is a study that needs to be considered.
All children thrive (educationally) in a strong school setting (academic and structure) until about the 3rd to 4th grades. Then, unless there is an engaged and supportive home, the chance of success is extremely poor even though the school may be strong. However, with supportive and engaged parenting no matter the weakness or strength of the educational system, the success rate is extremely high.
9) a very few homeschoolers are isolationists. VERY FEW. Most are active in their communities. The lost have not been corralled primarily into public schools. They also go to the store, the park, the library, the skating rink, the bowling alley, and they even live in our neighborhoods. There are charities that homeschool kids can get involved in (we visit nursing homes, work with an agency that trains service dogs for disabled children, and have helped with a Habitat for Humanity house project). There are academic competitions and athletic programs. And most high school homeschoolers I know have jobs.
If isolationism was a significant characteristic of homeschoolers, I'd understand the concern. But the few don't get to characterize the many, no matter how often people try to pigeonhole homeschoolers by pointing out the 2% who are on one extreme or the other.
This is all very good and commendable. Would that the media would show more of these good examples you have given.
Here is a problem. The earlier part of the post supported no mixture of putting the child into "unsupervised" or "non-religious" situations. Yet, in this section of your post, you show that is exactly what takes place.
Now, I know you are going to bring up "unsupervised," but that is the key that we both agree.
The engaged parent does not have an unsupervised child. No matter the school (home, private, public) the parent is involved.
Because of the interaction and the banter, the child of believers should gather discernment and carry the interaction and banter as a witness to their peers and other adults in all settings.
My very young son was standing in the grocery cart looking at a man buying cigarettes.
Unashamedly, my son blurted out, "Those are bad. They will kill you!"
Ah, the witness of the young.
