The reason is simple but needs to be made explicit: religious and other non-empirical ways of knowing don’t sufficiently respect the distinction between appearance and reality, between subjectivity and objectivity.
They are not sufficiently on guard against the possibility that one’s model of the world is biased by perceptual limitations, wishful thinking, uncorroborated intuition, conventional wisdom, cultural tradition, and other influences that may not be responsive to the way the world actually is. Faith-based religions and other non-empirically based worldviews routinely make factual assertions about the existence of god, paranormal abilities, astrological influences, the power of prayer, etc. So they are inevitably in the business of representing reality, of describing what they purport to be objective truths, some of which concern the supernatural. But having signed on to the cognitive project of supplying an accurate model of the world, they routinely violate basic epistemic standards of reliable cognition. There’s consequently no reason to grant them any domain of cognitive competence. Although this might sound arrogant, it’s a judgment reached from the standpoint of epistemic humility: that beliefs worthy of being called knowledge must submit to the tribunal of intersubjective, that is, publicly observable, evidence.
Objectivity is only gained through intersubjectivity. It is therefore well within the purview of organizations promoting science to call their non-empirical rivals to account instead of granting them implicit dispensation to make truth claims about the supernatural and paranormal. Not only that, it’s arguably an ethical obligation. Coming clean about the failure of non-empirical ways of knowing is an essential step towards assuming our collective cognitive responsibilities in the age of science and globally interconnective technology, when beliefs can have instant and far-reaching worldwide effects. This is Sam Harris’s crucial point against the politically correct public respect for faith, and it needs support and amplification, but in a way that doesn’t further alienate opponents of empiricism.