Home schooling is very rare because it is so unsuccessful. Most parents are not able to provide adequate home schooling. Also, there is more to school than just academics. Kids need to learn to interact with other people. If they always stay at home, they will always be dependent on their mothers for help.
Each family needs to make a decision based on the child's best interests. There are certain factors that can make public schooling better for some children. One of those is the exposure to many different instructors, and needing to learn to get along with teachers and deal with conflicts that may arise. This is good preparation for college, when students and professors may sometimes be at odds. It will also expose the child to other viewpoints than their parents'. And while home schoolers also get together for events with other home schoolers, public school does offer an easier chance for students to engage in sports, band, and other extracurricular activities, and engage with their peers.
Home school is much better as a student I have been both homeschool and gone to public school and homeschool is much better. Anyone who says that public school is better has obliviously not been homeschooled. First of all in homeschool you can move at your own pace. For instance say you are a very talented student and you are always done early. Then you are sitting around wasting time. If your are homeschooled then you can just move on. Also from the religious/atheist point you (and or your parents) can choose if you believe in atheism or a religion. And my final point is that you don't have to do common core or take the state testing which is a painful waste of time.