There's no inconsistency. As I pointed out, I didn't advocate for no homeschooling, but no homeschooling in it's current form.
There's simply no oversight to actually tell whether parents are qualified to teach children and provide them with a solid education.
I don't mind parents teaching them useless values (you could even argue that happens in public school as well), eventually the child will figure out that was worthless.
What can't happen is those children not getting the rest of the education they need to be productive members of society.
As I already pointed out, when that child becomes an adult and is unemployable, it's society as a whole that bears that burden.
While schools were closed the vast majority of them moved online, and classes continued remotely. It lacked the social interaction factor, which everyone agrees is far from ideal, but we actually had a health emergency. It's definitely not the norm.
We have literal decades if not centuries building an improving educational systems, updating them year after year as society moves forward. The curriculum nowadays has little resemblance to what was taught in the 1950's, for example.
Also, the border/education analogy is simply nowhere near the same ballpark. Separation at the border means they're still searching for the parents and kids to reunite them. Kids going to public school spend half a day outside the house, see their parent daily, sleep in the same house, spend weekends together. Like, not even close.