I was homeschooled for a little over a decade of my formative years and unsurprisingly I heard plenty of odd criticisms of it but I have to say I don’t think I ever recall Holocaust denial being a part of the standard repertoire:

Every bit of commentary in the age of social media has to be turned up to 11, of course, so I suppose it is unsurprising that we might start associating something perfectly fine like homeschooling with something very bad like anti-Semitic conspiracy theories. The viral popularity of the tweet certainly shows that the writer hit the nail on the head, or at least that she hit a nail on the head. I guess there really are a lot people out there who believe homeschooling is a front for the ANP, or something. I bet you the people who believe that were educated in public schools.
There are a few things worth noting about Ms. Claire’s rather shallow little epiphany. The first is her indignation that “real teachers” have to “go through years of training and state certification” while comparatively uncredentialed parents can just “be the teacher.” We know from decades of empirical data that, relative to their peers in standardized education, homeschooled students tend to perform just as well and often better by most common aptitude metrics. The big secret here is that educating children just isn’t that hard. It is actually shockingly easy to do. You do not need a specialized pedagogy or “years of training” to do it. You can just, you know, do it. Parents figure this out pretty quickly when they decide to homeschool their children; all the opaque mysticism of education fades pretty quickly when you realize that teaching is just carefully explaining things. Boom, done: Your kid is educated.
But if it’s so simple that most people can do it, then why the “years of training and state certification?” A big part of that is assuredly what economists call “gatekeeping,” the practice of restricting access to market participation in order to drive up the economic power of those already within the market. It’s actually relatively easy to become a teacher in most states—they don’t ask too much of you—but the teacher’s unions (who of course write all of those rules anyway) want to ensure at least something of a bottleneck at the point of employment, to try and drive up the salaries of their union members.
Then, too, a secondary benefit of those requirements is that it drives up the cachet of the teaching class; putting a bunch of unnecessary rules in place will always make something seem more complicated, and thus more indispensable, than it really is. I mean, here’s your proof: Julia Claire has become so convinced of the spectacular power of educational credentials that she is only capable of comparing uncertified teachers to Holocaust deniers!
Hatred of homeschooling, of course, is nothing new, but as ever it makes many of us very glad that it is indeed an “accepted practice in this country.” That wasn’t always the case; up until really the mid-1980s it was relatively difficult to homeschool your child in most states. A concerted effort by homeschooling groups and determined parents changed all of that. Here we have a pointed reminder that there are still many people who would prefer that homeschooling be broadly prohibited and that the state possess a monopoly to control the minds of your children. Thank goodness we can say to these people with impunity: No, I should be the teacher.
When I was a kid, I was simultaneously home-schooled and public-schooled. Not only did my parents check over every bit of homework I ever did for my public school classes, but they also gave me (and my siblings) additional lessons and homework, moving us quickly and significantly beyond the capabilities of our public school classmates. I attended both public school and college classes in high school, graduated from high school when I was 15, and finished my undergraduate degree at Stanford at 17.
I can't say I didn't resent my parents' determined oversight of my education when I was a teenager, as I didn't, at the time, appreciate the prioritization of my education over my social life. But I have been nothing but grateful for it since. Having experienced firsthand many years of education in both a public school and a home school setting, I can say with authority that my home schooling was orders of magnitude better -- much more responsive to my specific, individual needs and much less wasteful of time. Neither of my parents was in any way religious, and none of my home schooling was "Evangelical" in any way.
In her tweet, Julia Claire conveniently ignores the fact that indoctrination of children is rampant in public schools. Of course, people who do gloss over this fact tend to do so because they approve of that indoctrination. If public schools began instead to instill political points of view they disapproved of, I've no doubt they'd change their tune very quickly.