Why is the Latin New Testament authoritative for the Catholic Church rather than the original Greek? Just wondering why they chose Latin instead of Greek to be the source of truth of the texts, and instead added this abstraction layer when they were so close to the Greek culture at the time?
Pope Pius XII explains in his 1943 encyclical on biblical studies, Divino afflante Spiritu, §21:


  this special authority or as they say, authenticity of the Vulgate was not affirmed by the Council [of Trent] particularly for critical reasons, but rather because of its legitimate use in the Churches throughout so many centuries; by which use indeed the same is shown, in the sense in which the Church has understood and understands it, to be free from any error whatsoever in matters of faith and morals; so that, as the Church herself testifies and affirms, it may be quoted safely and without fear of error in disputations, in lectures and in preaching; and so its authenticity is not specified primarily as critical, but rather as juridical.


Even from a "critical" standpoint, St. Jerome had access to manuscripts that are no longer extant; his "New Testament scriptural texts were within a few generations of the original manuscripts penned by the Apostles" (Dr. William G. von Peters, editor of the new reprint of the Douay-Rheims).