The Limitations of Abstract Reason
I am actually very sympathetic to the role of reason in all political discourse probably more so than the Hazony, the author of the quote in the OP.
After all there is not much sense in developing, or uncovering, rights against slavery and in favor of the equality of women, for example, if those rights are not meant to be "inalienable", that is, universal. And if they are universal, then surely what that means is that our abstract reason, rather than tradition, requires this to be so.
tradition is not so monolithic as the account supposes, but varies from group to group, leaving a need for consistency between traditions — Banno
There is actually a strange relativism within conservatism I think - if we appeal to tradition in one society that tradition is going to differ - sometimes widely - from traditions in other societies, and now how do we converse with each other, unless we again appeal to a faculty of reason which can appeal to universals?