No, children should not be homeschooled - they should go to public school
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There is a lack of all-around expertise in homeschooling
Perhaps a parent is really good at math, but can they teach English as well?
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An issue that parents may run into is their ability to teach in all subjects. The advantage of public school is access to multiple teachers, each educated in their own individual subject. A parent teaching their children must learn how to teach everything, not just what they themselves know about. This may prove to be an education barrier, as parents will not be able to help their kids. Students must seek help elsewhere. This defeats much of the purpose of homeschooling. A parent who wants to homeschool must be willing to learn a lot themselves, and not all are ready or prepared to do that.
Just because a parent does not specialize in every subject should not scare them away from pursuing homeschooling. They can teach to their knowledge, and use an online source to help with the rest - much like what often happens in public school. Independence and a desire to learn is created and fostered naturally.
[P1] Homeschooling requires parents to teach all subjects. [P2] Parents don't always understand all subjects.
Rejecting the premises
[Rejecting P2] While this may be the case, it is not necessarily a big problem.