I've only read the last page of this thread recently, but it seems to me, GuitarStv, that you could have been more specific about what kind of "false equivalence" you were talking about.
I think that the false equivalence is between different kinds of potential abuse:
- In a B&M school/other group setting such as coaching or scouts, it seems that the potential abuses will range from poor instruction quality, verbal abuse and humiliation by other students or authority figures (almost certainly the most common), to physical abuse/beatings (probably the rarest and most easily caught), to periodic/recurrent sexual abuse (most serious).
The potentials for abuse outside the home are scary to a loving parent, because it feels that no matter how a good a parent you yourself try to be, you can't completely control the possibility that an aide at the nursery school might molest your toddler, that the kids in your son's third grade class might bully him at recess, or that your teen daughter's beloved skating coach might slyly groom her for years of abuse. If you know that you yourself are good, then you can cut down on this potential abuse 100% by keeping your kids at home.
- Homeschooling abuse could include all of the above, and at its worst, could also include crazy stuff like starvation, imprisonment, severe beatings, with a higher frequency and permanence than a child would get by attending school... school abuse will be periodic and temporary, but a homeschooled child can't get away from the abusive home for any respite.
So the potential abuses are much more severe in homeschooling, which leads pro-B&M school advocates to fear the consequences of unregulated homeschooling. If you are a good teacher or coach, you know that kids from sketchy homes can be safe while they are with you, they can get a good free lunch and maybe breakfast at school, and watchful reporting can rescue a few from abusive homes.
The only sure way to prevent and stop abuse is to make sure that many eyes are on the kids at all times, and that the kids know how to speak up. It's a puzzle: kids ought to have access to a variety of trusted adults in whom they can confide; yet the introduction of each new adult brings a certain (hopefully low) probability that they will be an abuser.
Maybe homeschool families ought to at the minimum, submit their kids to annual testing/interviews... nothing too severe, just checking for progress over the previous year in basic literacy/math, and maybe a 15 minute chat to hear about what the kids studied that year. That wouldn't help with the abuse, but it might help parents and school systems make better academic choices. Also every homeschooling kid ought to take a short class every year informing them about their rights over their own bodies, basic safety, and how to report any issues (as should regular school children).
I think the best solution is to move away from the all-or-nothing mindset (constant testing and ignoring individual student variations in the public schools, absolutely no regulation of homeschooled students) to providing a range of compromises that would bring oversight and standards to homeschoolers, yet allow for more presence and roles of parents.