How do your kids adapt to social interactions with kids of their age, spending 24/7 with your family might be tiring and in young age there is a big difference between 3 and 5 year olds, I think they need to interact with kids of their age and different cultures to be better adapt in future life, that's just my opinion, I might be wrong?
I'll need to make the decision about homeschooling in a few years. Do you have any studies you can share that support that conclusion?
At face value, it seems more difficult to socialize children than at traditional school with hundreds of daily social interactions from a wide variety of backgrounds, personalities, and teamwork opportunities.
My knowledge of this is rooted in having been involved in the online gifted homeschoolers community. I was briefly Director of Community Life for The Tag Project. http://www.tagfam.org/ So, you can take my word for it as a SME or you can contact Tokenadult and see if he can hook you up.
I do think your assumptions are in error. Good socialization is not about a wide variety of superficial relationships. It is about having positive interactions that teach one what one needs to know. I do know that studies show that kids who go off to boarding school do best if they figure out how to artificially replace the natural family unit with a close group of caring friends. But I don't have links to anything. That is just remembered off the top of my head.
There probably are numerous advantages to homeschooling, but I have a hard time finding convincing evidence. Either it's anecdotes from a small community of homeschooling parents or a study commissioned by an organization that has a vested interest in homeschooling, or authored by a leading member thereof. Significantly, I find that the people who share positive anecdotes are in higher wealth brackets and very well-educated, and I'm not aware of any studies that control for this.
You're not wrong - there are a huge number of homeschool groups, co-ops, classes, etc. Most homeschooling families actively try to socialize their kids with art classes, sports teams, and so on. There tends to be more supervision as well so there's less bullying too.