Someone wants to educate their children at home, in Germany that's not ok. In the US it is, so in the US they get some level of asylum.
These folks aren't some terrorists, they're not hurting anyone... seems like a situation where there are two different approaches, not some serious crime.
It also is a case by case basis so who knows if it holds up in court for long.
Edit: Looks like they lost the asylum part of their bid:
https://abcnews.go.com/US/home-schooling-german-family-allow...