Luther says that public education is great; it just fails due to parents, students, home life, etc... Let me translate that for you. That means public education is a failure. If a system fails to work in the real world, it is a failure. If a system fails to take its userbase into account, it is a failure.
Luther thinks that he is defending public education, but he's actually just referencing the things that it has been unable to overcome, thus the things that make it a failure.
Then he has the cajones to say that it's a failure, which obviously proves we don't need to replace it.