If you have bad social skills, you should go to a public high school. It would be a good experience and it would make you better at being social. I was homeschooled from 5th grade and before. So far going to public school has helped me a lot socially. But if you're involved in a lot of activities and you already have some good social skills, you can rule out this reason.
It also depends on where you live. You can look up reviews on what public school you would be going to, and you could see how good the school is. If it has pretty bad ratings, home schooling would be the better option.
Another pro of public schools are the teachers (most of the time). If your parents/guardians aren't doing a good enough job of teaching you, the teachers at the school (depending on the rating) could be a lot better and help you understand concepts more.
Home schooling and public schooling all have their pros and cons, but the better option depends on many factors such as location, teacher, social skills, etc.
