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From ST:TNG "The Game", when the crew welcomes back Cadet Wesley Crusher on vacation from the Starfleet Academy:
PICARD: Quomodo tua Latinitas est?
WESLEY: Praestat quam prius.
PICARD: Oppido bonum. Your Latin has improved.
As Picard would ask, "quid studere latina in Academia?". Why would they bother? Both as far as Latin being a dead language, AND with the Federation having one of them Universal Translator doohikeys.
I'd prefer in-Universe answer, but will take any.
I don't know that there's an in-Universe answer, however ...
Latin is incredibly useful for being able to comprehend a word's (potential) meaning without having an explicit definition, rather than just transposing words from one language to another, which is the function of the Universal Translator.
Additionally, it helps with critical thinking and analysis to understand how another language conjugates and modifies depending on various scenarios. In this, it would be more of an academic exercise, but not uncommon in today's academia whereby it's often required to have a secondary language as part of one's study.
Furthermore, in the days of a Universal Translator, depending on technology puts you at it's mercy for communication and the lack of skills to operate without it leaves you with a potentially critical vulnerability. I don't think Latin is going to help with extra-plantary languages though.
TangoOversway commented:
I don't mean with translating at all. I mean in understanding language, including roots, structure, and derivations.
A language is not just a dictionary of words and their meanings. It is a highly complex model of communication with various rules described in grammar, orthography, pronunciation, sentence forming, etc. Now, the thing is that these rules tend to be more different for languages that are less related.
Two related languages may have an almost identical structure and a different vocabulary. Example: Italian and Spanish
Another pair of less related languages will have a different structure, grammar, etc. but at least they will have the same concepts - sentences, gender, numerals, and so on. Example: English and French
Less related languages would have a few quite different concepts. For example, most languages have singular and plural. Slovene has singular, plural and dual.
It's easy to imagine what kinds of differences may occur if we compare two completely unrelated languages. I don't have the knowledge to make the comparison, but I can assume that the list would be quite large for, say, Japanese and Portuguese.
Now, since you mentioned Latin specifically, I'll give one example why would it be useful. A native English speaker without knowledge of any other languages would (probably) have difficulties with noun case system present in some modern languages (e.g. most Slavic languages) since that concept is almost extinct in modern English. On the other hand, someone who had learned Latin wouldn't have too much trouble to figure it out. They would just say Oh, Родительный падеж, that's Genetivus, right And I don't mean just to know intellectually what that is - I mean to understand it, to grok it, if you will.
Understanding foreign concepts is the hardest thing when learning new languages. Now, why would Starfleet officers have to understand various concepts of languages and communication, I wonder? Could it have anything to do with all those first contact situations and the fine details of diplomacy? I would bet that they don't only learn Latin, but also other classical languages from Earth and other Federation planets, at least to some level of knowledge. Wouldn't it be strange if Starfleet trained its officers to attempt to understand alien communication without first training them to understand Earth languages?
Why would they bother? Both as far as Latin being a dead language, AND with the Federation having one of them Universal Translator doohikeys.
Universal Translators do have limitations. Just remember Darmok, and Jalad... at Tanagra.. Actually, the main plot of that episode is about a language with incredibly different concepts - a difference which their Universal Translator was unable to handle.
I think the better question is: Why not?
If we look at the cadets of the Starfleet, every single one seems to be able to do Quantum Math and other fancy stuff. Seeing that, we can assume that the overall IQ has increased over the centuries. As such, teaching languages seems trivial.
As already pointed out, learning different languages helps with bending your mind around communications in general. I also assume that they learn basic "Federation languages", too, like Vulcan. In general I'd assume that the schools and academies work on the basis "we throw everything at the cadets, if 0.1% needs that knowledge, it's worth that" since every single member of Starfleet seems to have a very broad basis of common knowledge.
I'd like to propose a simple answer: Because Latin used to be the international language of intellectuals. So, of course, somebody who's education is a bit more "old school" might first think of using it as a possible fictional intergalactic language. Other's wouldn't make this sort of mistake, as you will see more modern sci-fi shows using hybrids of Chinese and English as their intergalactic language of the future, which is more plausible.
Since in the Star Trek universe computers can do pretty much everything, including advanced math and translating, it seems that people tend to study stuff pretty often just for fun. There isn't nearly as much focus on just studying the things that will 'get you ahead' in your career. Every character in Star Trek from TNG onwards seems to have a hobby, often one that would require a lot of study to be good at in our world. Maybe Picard and Crusher both took Latin as a fun elective.
