"Peers" as defined in public schooling means "people within plus or minus 12 months of your age, and with virtually the same experiences and knowledge". That's hardly "diverse", and moreover is hardly reflective of the kind of people you interact with in real life as an adult. Homeschooled kids regularly interact with adults and children much older and much younger than themselves, gain a far greater range of experience, and are far more effective adults.

I have a hard time imagining what you mean by "pushing them farther than parents think they should be pushed". Homeschooled students far exceed public schooled students in academics. I guess you are referring to the condom-on-banana stuff and the lectures on white privilege, right? In what other areas are public schools actually considered to be "pushing the boundaries"?