Fact is, homeschoolers have an advantage of not having to try to stick their square pegs into round holes.
I have a daughter-in-law teaching 4th grade who is constantly at odds with the other teachers who are spending tons of time on things other than teaching actual content, which she feels is the entire purpose of the school. Her frustration level is so high, she needs time to cool off from the pressure. They won't pay for a workshop to improve teaching techniques for failing students, so she's doing it out of her own pocket and stays after school long hours to help them. There are many, many really dedicated good teachers who care, but administrations and unions don't really support them well.
If my grandson were still in public school, he'd probably be in third grade still, but he's finishing up 7th BECAUSE he doesn't have to fit into a round hole..... We take time to do things right, no matter how many times we have to do it.
I don't think this is arrogance.... but it is determination, and it is love. The schools don't love our children.
I don't think that we are disagreeing about homeschooling. We don't homeschool because we have a good Christian school close by. However, were the situation different, we would homeschool.
There is sometimes misplaced confidence by homeschoolers in their abilities and a distain for experts which I sometimes see as unhealthy in other situations. However, that doesn't apply in homeschooling situations where any dedicated adult can adequately educate young children.