Control for socioeconomic status and homeschooled kids tend to do worse in STEM subjects. Even your link which mostly doesn't control for SES and therefore is very biased says this. Therefore you can't say that it is better on every metric, if you think that STEM is important then homeschooling is bad.

> Qaqish (2007), on the other hand, examined the ACT math scores of college-bound students and found, while controlling for background variables, that the conventionally schooled performed slightly better than the home educated.