Children can receive a higher quality education
The curriculum is highly controlled in homeschooling, ensuring that it is valuable information.
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The Argument
Public school education cannot necessarily guarantee a quality education, or a learning route that parents would like for their child. One study showed that "in a recent comparison of SAT scores, homeschooled children averaged 568 on the verbal test and 525 on the math; the national average was 506 on verbal and 514 on math."[1] This may be from the ability of parents to tailor a child's curriculum and allow them to learn even more. A child can move at their own pace, rather than waiting for others or being dragged along before they have a full understanding of the subject.
If parents have certain values they would like to instill within their children, they can incorporate this into the curriculum. This is especially beneficial for those with religious morals, as most public schools do not incorporate that into their education. Education is able to be tailored to the family.
Counter arguments
Just as not all educations received in public school may be high quality, the same goes for homeschoolers. Homeschooling may not allow a child to learn as much as they would like - it all depends on the learning style of the child and the teaching style of the parents.
Proponents
Premises
[P1] Homeschoolers score higher on the SATs.
[P2] Higher scores likely come from tailored education.
[P3] Homeschooling is better for students.
Rejecting the premises
[Rejecting P3] This depends on the student and the quality of the teaching.