Obviously, the government institutional schools aren't teaching. It's the parents who are.
Let’s turn this on it’s head..”If home school/religious school/private school don’t learn, then they are failures. Every method of teaching has failures. If you’re goal is 100% success, everyone is a failure. Or are you going to tell me that every home schooled (or private school, or religious school) student succeeds?
Your last sentence “Obviously, the government institutional schools aren’t teaching. It’s the parents who are.” is simply not true. Even though I and my wife helped at home, I will guarantee you that I did not teach my kids algebra, trigonometry, or biology. The teachers at their high school did, just as their elementary and middle school teachers did most of the teaching in their subjects. The fact that we helped them study at home in no way refutes that.