I wouldn’t be surprised if I turn out to be wrong, but I was taught the causal chain was:

1. The Romans spoke Latin 2. Catholic church based in Rome, did everything in Latin 3. Between tithes and indulgences, church got rich and powerful 4. The rich and powerful keep learning Latin to keep up to date with news from the other rich and powerful

latin was used because it was the language you used to write important stuff, it was with the creation of france and Germany that other language were upgraded in social status