This page contains a link to a transcript of a lengthy but extremely helpful series of lectures John Frame gave on the relationship between Christ and culture. Although I may not agree with all of the practical applications of his perspective that are found at the end of the document, it is worthwhile reading.
Here’s what Frame says about the fact that secular humanism bounces back and forth between moral relativism and dogmatism based on their own autonomous moral judgment:
The moral relativist side of secular liberalism stems from the fact that, as Dostoyevsky noted, if God doesn’t exist, anything is permitted. But such universal permissiveness is a recipe for chaos, one which even secularists cannot easily accept. Thus they seek to replace God with another supposed absolute. (Scripture calls this process “idolatry.”) That absolute is, in most cases, their own autonomous moral judgment. Hence the “dogmatic” side of secularism. But when that dogmatism fails, when the secularists’ own judgment proves untrustworthy, then they revert to relativism: “Oh, well; nobody really knows.” Relativism and dogmatism: these are the Scylla and Charybdis of secular liberalism. Strictly these are inconsistent with one another. But they supplement and need one another. The secularist bounces back and forth from one to the other as on a pendulum (p. 13).