You should remember that a child who is homeschooled probably have parent(s) that are least reasonably fairly well to well educated, whereas a child walking into a public school may have either well or poorly educated parents. If one wants to homeschool a child, they have that right, but then comparing that child to what comes in the door in a public school is an unfair comparison.
My wife is the product of the Catholic parochial school system, which is quite good here in s.e. Michigan. When it was time to have our kids start school, we had a decision to make, and even she said going to public school would be our best choice as we live, and I taught, in a good district. All three of our kids went to college with our oldest being a college professor, our middle child being a nurse who works for Hospice and co-owns an insurance agency, and our youngest owning his own construction company. Public school didn't seem to hurt them one iota.
There's also a financial reality that hurts public schools in particular, but I'll not get into that now.