Obviously as an extract the quote can only single out certain aspects of the thing. Here Latin has arbitrary order, history, beautiful etc. Also should have said it is the common root of or at least strong influence to European language.
But still why today learn it depend upon the key question. If I do not learn it what is the impact. Not sure. That is my answer.
Learning Hebrew for bible reading. If forced German for philosophical work. Latin? Not sure.
Latin was the common international language of Western Europe for more than a thousand years after the Roman Empire collapsed. Even until the 19th century there are some (admittedly by then a bit rare) examples of major treatises composed in Latin rather than in a national language.
There is a gigantic body of literature, science, history, philosophy, and so on, all written in Latin.
If civilization survives long enough, people will probably still be studying English thousands of years from now for similar reasons, even if there are no more native speakers.
But still why today learn it depend upon the key question. If I do not learn it what is the impact. Not sure. That is my answer.
Learning Hebrew for bible reading. If forced German for philosophical work. Latin? Not sure.