Unbelief does not teach the faith. Unbelief can undermine the faith. Faith alone is used by God to communicate the faith to others. There are no exceptions. Unbelief, no matter how learned or erudite, cannot give others what it does not have.
Pedagogy is an asset provided it is built on faith.
But without faith, pedagogy is not only a liability, it becomes seduction. Like Mary, a catechist teaches almost without catechizing. Our Lady did not conduct classes and the number of her spoken words recorded in the Gospels is very small. Yet St. Augustine does not hesitate calling Mary a living catechism, Catechisms vivens. Because that is what she was.