I was k-5 public school and they failed me. Parents put me in Christian school for 5-9. It was eye opening just how far behind I was going into private school and by 8th grade graduation I was valedictorian. After 9th grade my parents couldn't afford private any longer so back to public I went. I was so far ahead of everyone that I basically cruised through HS and ruined all study habits and progress. Here's one for you, the science curriculum I already knew inside and out. After a test the teacher agreed and just let me do her college course work. At the end of the semester that bitch gave me a B because she said "it was all so easy for you that you gave no effort. So I had to mark you down for effort". So I did her college masters work for her (one course anyway), aced it -- all totally because of the private school curriculum in the past-- and I get a B. So pissed I didn't try anything else then on.
Anyway, I home schooled my kids through both Christian Liberty academy and charter school programs locally. Socializing came from neighborhood kids, 4h, scouts and ect. Don't let the establishment bully you into thinking because you home school that the kids are isolated in a bubble. That's horsecrap. That message comes from the very people who simply want the power to indoctrinate and are afraid to lose it.
Homeschooling kids has better outcomes academically. The establishment isn't making me think one way or the other, I base it on actual experiences in my life.
Some private schools are great and others not so much, same applies to public schools.
You still had your kids in programs and lived in an area they could socialize with other kids which is great. Unfortunately, not all parents do that which creates a socially stunted individual.