In order to make a decision to teach your child at home or send them to the public education system, you often have to look at home school versus mainstream schools objectively. Here are two different things that you should consider when trying to decide which one would be best for your child.
First, do the socialization your child will get because you decide one way or another. Social media will be limited to a certain amount of money when you're home to school, but it's certainly possible for you to join groups like minded people so they can interact in some way or another. Yes, your child will be a lot more social education in the public school, but you will not control the environment in which the social organization will take place. This is a great decision and probably one of the most important things that you are going to do as far as home schooling in public schools.
Another thing to keep in mind is to develop your child educationally. In public schooling, the whole course goes through a curriculum at the same rate, regardless of the personal development of each child. Homework allows you to control the speed your child moves through a curriculum. This will help them develop more like their education and to combat boredom from taking too long with subjects they know.