The author is repeating an old, hoary chestnut from the days of Edward Gibbon about a sudden decline in Roman prosperity after the conversion of the Empire to Christianity. This is basically a false rumor which seemed believable in Gibbon's Age of Enlightenment, but he had to work hard to present any supporting evidence for it, including fabricating the myth of the destruction of the Library of Alexandria.
In reality, the Empire was already in cultural decline after the 2nd century (for example, we know of no updates to Roman law after the Institutes of Gaius circa 170 AD), but the economy was sustained through the 5th century, leaving no room for Gibbon's theory to find success. Here's one academic analysis:
Until fairly recently it was believed that the entire economy of the
empire was in severe decline during the third and fourth centuries,
with a falling population and much land going out of use: two things
that would undoubtedly have weakened Rome’s tax base, and hence its
military capability, long before the period of invasions. However,
archaeological work in the decades following the Second World War has
increasingly cast serious doubt over this interpretation. In most of
the eastern Mediter- ranean, and in parts of the West, excavations and
surveys have found conclusive evidence of flourishing economies under
the late empire, with abundant and widespread rural and urban
prosperity. (Bryan Ward-Perkins, The Fall of Rome and the End of Civilization, pp. 41-2)
How did Christians actually view "ancient learning"? It's well-accepted that while much of Greek science and literature was kept alive in the Muslim world, the survival of Latin literature was thanks to a large and long-lasting project by the Christian emperor Charlemagne:
Our whole knowledge of the ancient literature of the West is due to
the collecting and copying which began under Charlemagne and almost
any classical text that survived until the eighth century has survived
until today. (Kenneth Clark, Civilisation: A Personal View, quoted
in Thomas E. Woods, How the Catholic Church Built Western
Civilization)
By this time, only Christian religious were literate.
Widespread literacy in the post-Roman West definitely became confined
to the clergy. A detailed analysis of almost 1,000 subscribers to
charters from eighth-century Italy has shown that just under a third
of witnesses were able to sign their own names, the remainder making
only a mark (identified as theirs by the charter’s scribe). But the
large majority of those who signed (71 per cent) were clergy. Amongst
the 633 lay subscribers, only 93, or 14 per cent, wrote their own
name. (Bryan Ward-Perkins, The Fall of Rome and the End of Civilization)
But what exactly happened from the 4th to 8th centuries that limited literacy and interest in classic literature to the Church? The answer is not from antagonism by Christians, but from the total collapse of the imperial system. The city of Rome at the peak of the empire housed as many as a million people (Neville Morley, Metropolis and Hinterland: The City of Rome and the Italian Economy, 200 B.C.-A.D. 200, ch. 2). After being captured in 410, the city was sacked and decimated; Procopius writes that at one point during the Gothic Wars, Rome was totally deserted (Gothic War, III.xxii).
With the massive population, financial, and military losses, basic technologies also suffered. Obviously, paper manuscripts from this period have disintegrated, but other technologies still survive and tell a detailed story. Rome's boundless production of fine pottery, which can still be found at hundreds of archaeological sites and were certainly available for cheap to all levels of society, vanished entirely during the 5th century. Roof tiles, also found on the humblest homes, follow a similar pattern:
In the fifth and sixth centuries, tiles, which, as we have seen, had
been very widely available in Roman Italy, disappear from all but a
few elite buildings. It may have been as much as a thou- sand years
later, perhaps in the fourteenth or fifteenth centuries, that roof
tiles again became as readily available and as widely diffused in
Italy as they had been in Roman times. In the meantime, the vast
majority of the population made do with roofing materials that were
impermanent, inflammable, and insect-infested. (Bryan Ward-Perkins, The Fall of Rome and the End of Civilization, p. 109)
Economic and demographic collapse, not Christianity, was responsible for the destruction of the libraries of ancient Rome. The Church, sustained by donations from surviving landholders, was solely responsible for saving Latin literature.
