Why so many people are so convinced of this, and not only in the “first world,” is not entirely clear. Obviously, part of the explanation is the penumbral hold that the Christian progress narrative still maintains over our thinking. On this account, for all the bumps and glitches that humanity is bound to face along the way, history, too, is a progress toward a global society. One does not have to be a person of faith to adhere to this view. To the contrary, it was that stern non-believer Raymond Aron who proposed that what made modern times unique was that they were the era of universal history.
...In other words, almost anywhere on the squishy bog that is the contemporary intellectual landscape—right or left, technocratic or legalistic, unilateralist or post-national—we will most likely find ourselves sinking into the muck of one modern iteration or another of Hegel’s ideas about universal history and the theodicy that accompanied it. That the Greeks, or, indeed, great Renaissance political thinkers like Machiavelli and Guicciardini, who essentially believed that history was a series of cycles, not a progress, would have laughed at such a crude account is worth pointing out, if only as an at least partial vindication of the intuition of educated pagans, like Celsus in the late Roman empire, that Christianity was not going to be an intellectual improvement over Greek philosophy. But as a faith, Christianity can hold that we are progressing toward a day of final judgment and the end of history without having to provide empirical grounds for its claims. The adherents of secular progress narratives, however, can plead no such justification.
The article as a whole is great, but I have my doubts over whether it's really fair to describe modern political progressivism as a direct descendent of Christian teleology. I mean, yes, Christianity envisioned an obvious end point to human existence, located in time, but in practice, "progressing toward a day of final judgment" typically meant sitting around in cultural stasis, watching the unspooling of the world's thread—a state of affairs that endured for much longer than our post-Enlightenment progressivism has yet existed. The Middle Ages (frequently used as shorthand for a representative summary of a thoroughly Christian culture in action, of course) were content with the understanding that since divine truth had been revealed centuries earlier, there was no need for radical social change or technological innovation while awaiting the Parousia, and the Christian view of human nature itself had of course always been pessimistic. Until the empirical fruits of scientific advances began to appear, I don't know that a truly modern sense of progress can be said to have existed.