Seems like you're coming at this from a religious angle, which is completely fine. Everyone has the right to educate their children however they see fit, including whether they'd like religion to play a central role in that.
However, essentially every data point in this entire infographic is either irrelevant to the point you're trying to make (that home schooled kids perform better according to most metrics in and out of school), or is simply an observable correlation which is more meaningfully influenced by other, primarily socioeconomic, variables. Further, some of the data is flat out misrepresented or is 25 years old at this point and has been subsequently contradicted by more recent studies (e.g. Harvard study in 2010 showed that public school kids are more likely to go to college, 2014 analysis of ACT scores shows that home schooled kids outperform public school but get outperformed by private school, etc.).
The real driver behind the good outcomes that can be observed in home schooled children is that they have typically well-educated, engaged parents who participate in their education. They have parents who hold them accountable to succeed in their schooling, which is a fundamental head start over a large portion of the children in public schools. If you could drop the same family dynamics into the household of every public school student, you'd be amazed by the shift in test scores, grades, etc.
All this means is that being an involved parent is important, and that effect carries over to public and private school kids also. There aren't a lot of shitty parents out there who suddenly decide that they want to invest time in home schooling their kids, but there are a ton of them who allow their kids to flounder through public schools until they're legally able to drop out without ever having a meaningful conversation about education. What you're left with is selection bias for this type of empirical comparison. You want to get closer to showing causation? Control for all of the socioeconomic advantages that home schooled kids have over a great deal of public school students. You'll find that schools do well teaching kids who are ready to learn, especially in science and math.
Anyway, I don't have anything against people who want to home school their kids or have a parent stay home with them instead of sending them to daycare; that's a choice every family can make for itself. What bugs me is when people act like their way of doing things is obviously superior and use propoganda to disseminate their ill-founded dogmas. There are plenty of observable advantages to both daycare and regular schooling but that doesn't mean that home school isn't right for certain families, just as the success of some home schooled kids doesn't mean that all kids would be better off being taught at home.