No, children should not be homeschooled - they should go to public school
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Children miss out on high school athletics
They miss out on a free opportunity to play sports with their peers.
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Sports are often a very beneficial thing in a child's life. They instill good habits that will carry on into adulthood. They keep kids active. They provide a unique competitive social environment which may even benefit the child's college career. Approximately 50% of high school students in the United States alone play a sport. Most high schools do not allow homeschoolers to participate in these sports, depriving them of a very positive opportunity. High school sports are also typically free, so to access sports a homeschooled child would be required to pay a fee. Public school provides a wide variety of sports for children, allowing them to discover how they like to exercise and instilling life-long positive habits.
Sports are not for everyone. One should not be deterred from homeschooling simply based on the availability of sports. In fact, very good athletes are often homeschooled so that they can spend more time focusing on their athletics. They have the ability to work with a specialized coach during school hours. Public school kids would not be able to do this.
[P1] High school sports are generally a positive experience. [P2] Homeschoolers cannot participate in high school sports.
Rejecting the premises
[Rejecting P2] Homeschooled children can still participate in sports in they desire, and if they cannot this is not the end of the world.