Besides Mershon's excellent points--Latin, like Hebrew, Koine Greek, and Old Slavonic/Church Slavonic, is a "sacred language."
There is much to be said in favor of such--sort of like stained-glass windows, silence during parts of the Mass, and really good music--not the Mr. Rogers tripe.
In other words---tradition. Don't get me wrong--"tradition" is a perfectly acceptable answer. I just don't buy the theory that Latin has some kind of "magic advantage" over other languages with respect to the accurate tranmission of Church teachings and/or prayer. That is obviously bogus, as the key original dogmas of the Church had to first be accurately translated from Aramaic into Greek and Latin (Matther, Mark and John being Jews, and Luke being Greek).
As a practical matter, I think a perfectly acceptable approach is "both"---with local option.