When did Latin become the language of The Church and why?
Well for starters in the first 1000 years of Christianity it was a common language in the Western world the way that Greek was a common language in the Eastern world. It would have become the common way for people from different western areas to communicate with one another. Spanish, French, Italian, Portuguese all have their roots in Latin.
The language was preserved primarily as a common and unifying language within the Church. Catholics all over the world said and did the exact same things every Sunday and would know exactly what to do/say no matter where they were. Even today when we use Latin for various parts of the Mass we are connecting with our history, saying prayers exactly as they’ve been said for 2000 years.
Though the Mass is translated into the native languages of various regions of the world, the official text of the Mass is in Latin. All official documents of the Church are in Latin. Because Latin is a “dead” language that means it words do not obtain new meanings the same way that “living” languages do. With official Church documents in Latin it is easier to understand the meaning of even ancient documents and translation into various languages is easier without worrying about colloquial expressions in certain languages.
Latin is preserved in the Church because of its history and usefulness in the present day.
For further reading:
Pope John XXIII’s Apostolic Constitution (On the Promotion of the Study of Latin)*Veterum Sapientia *