Public schools are a much better choice for a majority of children. Home school isn't even regulated in many places. Also, children in home school are sometimes indoctrinated into extreme religious views and taught that they are reality. Public schools also allow students to socialize and intermingle, which is a very important skill.
I support the public school system. It is an inexpensive and effective way to educate your child. Children receive not only education in academics but they receive socialization skills that they will never learn from being educated at home. No matter how good of a parent a child may have, they need to learn how to react to other adults of authority. Public school is a wonderful way of doing this.
In public school, you get to interact with other people. People of different cultures, races, personalities and opinions. In class you get to hear what other people think, and you get to question your own opinion. Other students may have a question that you didn't think of and it could give you more ideas. Public school also prepares you for when you have to go into the working industry. In school, you may not like who you have to work with but you may no like the person you have to work with in your future career. Public school also helps you socialise, you get use to being around new people, and the change between schools is kinda like what it would be to change jobs.
Time goes by way to fast and having the gift/option of being with family is great. You get to learn more about what you are interested in hobbies and such. There are many great ways of getting to know others now days. You can meet friends at Co-op, church classes, sports, neighbors, family etc. My girls went to public school one until 4th grade and the oldest until 9th grade. They both like his better. We had no problem with our PS it's just I'm home so they can be as well.