One thing that concerns me about many pro-homeschooling comments is a kind of tear-down-the-schools attitude, as if schools were hopeless and irredeemable, despite the fact they're still educating 94% of students even at today's elevated homeschooling rate. Of course there are problems with schools, but on the other hand there are countless success stories, or at least countless non-failure stories, and educational outcomes tend to depend crucially on local factors, the location of the school and its socioeconomic environment.
I suspect that the vast majority of parents have neither the desire nor the capability to homeschool their kids. I certainly can't imagine my own parents doing it. In a sense, homeschooling is a luxury of the few. The absolute numbers can increase, but I don't think homeschooling can scale to the entire population. So whatever problems may exist in the schools, we have to confront and solve them, not just abandon them and pretend homeschooling is a societal solution. You might claim that hundreds of years ago, everyone was homeschooled, but I don't want to turn back the societal clock hundreds of years.
Another concern I have is the religious and/or political motivation of many homeschoolers. If homeschooling were just about educational outcomes for children, then we shouldn't expect homeschoolers to be disproportionately conservative in religious and/or political beliefs, yet my impression is that they are. It's certainly suspicious to me. And though I've had no involvement with K-12 education since I was in school myself, I've had a lot of involvement in higher education, first as an undergrad, then as a PhD student and lecturer. Frankly, the horror stories and conspiracy theories about left-wing indoctrination at universities are ridiculous and not based on fact or experience. So I'm quite skeptical of similar claims about K-12, especially since I saw none of that in my own childhood. (I recall being forced to say the Pledge of Allegiance every day, for all the good that did.) There's a type of person who's set off if you say "Happy Holidays" instead of "Merry Christmas" and consider that to be an act of war against them. There are still a lot of parents in the United States who reject biological evolution and would prefer that it not be taught in schools at all, or at least to be taught as "controversial."