I went to private school K-3 and 9th grade, public schools for the rest of the time, was never homeschooled but knew a few homeschooled kids, not enough to draw any valid conclusions about how well homeschooling worked for them though. as far as people shitting on public schools, yeah some of them are bad, but i think i just got insanely lucky--i was singled out as a "talented and gifted" person at my public elementary school for 4th through 6th grade and although it seems kinda elitist in retrospect, i loved it at the time. it was the same group of 25 kids every year, so i felt like i'd built up my own family of friends by the time middle school rolled around...and then i moved. 7th and 8th were ok, i didn't really have any inspiring public school teachers or anything--my 7th grade spanish teacher was the man, but other than that, meh...my 8th grade math and english teachers were cool too, they went out of their way to actually teach well and be friendly at the same time.
9th grade i went to an all-boys private Catholic school, basically because my dad went there in the 70s. hated it to the depth of my soul, half the reason i left was because we were shelling out six grand a year to go to a place which basically didn't seem any better than my old public school except for a pretty much ungrounded innate sense of overall superiority to everything. i had two really good teachers--one had a doctorate in theology, but was pretty charismatic/iconic anyway, and the other one was my dad's old bio teacher, who thirty years later was still the man. (if anyone's still reading this, don't worry, i'm getting to the point...)
10th through 12th grade were spent at my [new] hometown's public high school, which coincidentally seemed to be pretty much the best possible environment for education, even if it is an outlier overall. that's because i had two or three really good teachers every year, one or two who even gave a damn about the kids' problems outside school... had a badass old math teacher senior year and a granola-but-rational philosophy/history teacher, and everybody loved me by then because i'd pretty much solved the problem of how to get As in school and not piss anyone off. it was like, "warm" in general there. i learned to talk to other people without coming off as a douchebag or an emo prick basically because of the environment: everything was nice and clean, there was a new computer lab, new library, good friends to go around, nobody cared about how i flitted between different social circles at my liking because that was what i did. and i got a job at an easy-going supermarket too, where i finally learned to talk to older people and be respected, and basically learned to be a competent human being.
The moral of the story is that education by itself doesn't really do anything, nor does blindly deciding to throw yourself into society because that's what you think humans should do. it's the people that matter in the end: i think that for any student to succeed he has to eventually learn to be strong on his own, not for others but because he has a sense of pride, because he's heard from good people and realized why they are good. it's like america, not to piss off non-americans here but to emphasize the point--to succeed and be a hero in a free society you have to learn to think not just for yourself but for the future, have to learn what's important and what isn't and then not be a dick about what you consider important and what you don't. Education exists to build functioning free citizens--that's what public schools are for. Private schools and the notion of homeschooling basically exist because they think they can do a better job of teaching the young; and if they can, fine, but the public schools, if inept/corrupt/cruel, should be reformed to fix those issues. Here's how you do it: public schools should pay good teachers more; public schools, above all, need charisma, competence, and an environment healthy for developing personalities/ethics.
If you want to homeschool kids, fine, but do it correctly: they need to learn more than facts, they need to learn to exist. ...so that's my dickish opinion.