You can argue that Latin was important for a few reasons.
First, you can say that its use provided a link between the Catholic Church of the mid-1500s and the earliest days of Christianity. You can say that Latin was the language of Rome when St. Peter was the first bishop of Rome/pope and that it is important to maintain that link.
Second, you can say that it is important for a universal church to have a universal language. This emphasizes the unity of the church. If the liturgy is conducted in all sorts of languages, this unity is lost. This would allow Catholics to feel at home at any Mass in any country and it would allow Catholic priests and scholars to always have a common language in which to communicate.
Finally, you could argue that it was important to have strong distinctions between Catholicism and Protestantism so that people could have a clear choice and could be very clear on what it was to be Catholic. This would be better than blurring the lines between the two faiths.
Well Latin is a language that all of our modern languages come from even in Sanskrit(hindu) mother & father "Patar & Matar" are in latin to be precise through history man has tried to create holy languages the muslims have arabic, the hindus have sanskrit, shintosism has Japanese, early christians have latin, coptic christians have coptic. It is the balance of the religion and even english derives from latin almost every word derives from latin to be precise, italian, english, spanish, and even some russian derives from latin. Latin use to be the language of western civilization as well as other parts of the world. the council of trent did know what language to choose, actually many of the spartans spoke a form of greek/latin so I believe latin is our most well used language in the world ever since we became civilized...