Take it from someone who was homeschooled from pre-k through high school, you will absolutely not provide a better social environment. I was so unprepared to handle the social dynamics in casual, educational or professional that it took years and years of active work to put myself in a position where it wasn’t an absolute detriment to my success. I have no doubt you can educate your children well, it’s every other aspect of humanity that is typically missed out on and can lead to unintended consequences.