I think homeschool is better for a few reasons. Firstly there is the working at your own speed part. Secondly there's the part where you aren't around all the negative influences. Other kids won't be there to pressure you to do things that you'll hate yourself for for the rest of your life. You'll end up more moral. Me and my siblings were all homeschooled. We weren't hateful, we were very well behaved, and everyone said you can deffinately tell we're homeschooled because of that, and because we were all smarter than the other kids in the area. While they were struggling to read simple sentences we were reading full books.
There is really only one good thing about public school and that is that one (or two) people can't teach kids everything. For example, my mom is horrible at math and thus none of us kids are all that great at it either. But otherwise, all the negative influences from the other kids, their destructive and out-to-get-you attitudes, their pressuring, etc. are the worst things about schools.
Reality doesn't care if you believe in it.
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