They are not exclusive. My children go to public school, to get socialized and learn a broad range of topics including STEM and ELA. They also get homeschooled, to make sure they get a deep education in ethics, practical life skills (eg. gardening, cooking, making their own clothes, carpentry), financial literacy, civics, and art; subjects that are key to a fulfilling, self-reliant life but aren't always well-covered by formal education.