Disclaimer- I have worked with a Christian homeschool organization for a couple of decades often leading introductory seminars.
When asked “What about socialization?” I habitually respond “ Yes that is another excellent reason to homeschool.” After letting that set in on their dumbfounded faces, I then I explain the evils of peer pressure and bad company; contrasting that with home-school graduates who are polite, outgoing and able to interact with a diversity of ages and backgrounds. I tell them of my own children’s “church friends” 4-H and clubs. In short order I explain to them that parent supervised and limited socialization leads to the best outcomes for a child’s social development, why just look at a public school and ask: “How’s that working out?”
May I recommend that you add this to your reasons: In public (and most private) schools, children are surrounded by people of the very same age. There is very little diversity. In authentic "social" situations, we are surrounded by a wide variety of ages. It is more normal to be in the later situation.
My sons were very comfortable around adults - and as a result, adults were very comfortable around my boys.
Homeschooling put my children in all kinds of social situations that were "normal" and rarely did they see artificial segregation by age.
In short, "Homeschooling works!"