Some pronounce the trailing "i" in Latin-derived words (e.g., "Gemini") as a long "e" and others pronounce it as a long "i." I was taught the long "e," but is this mere preference or is there a firm basis for one or the other?
If you're familiar with the wide variety of pronunciations of English words, it probably won't surprise you to know that Latin — which has arguably been spoken for longer and in more countries — should also suffer the same fate.
Nobody knows how Latin was originally spoken.
There is no firm basis, therefore, for any particular way of speaking. Latin has been kept alive more by the Church (in her many denominations) than any other body, in which an end of i is pronounced with the long e, possibly best known from Enigma's "Sadeness":
Long e works better when sung (a long i having more than one part to it, sounding more like aahyee when sung slowly*).
However, I blame just one thing in particular for spreading the i sound, and it's this:
We all get to learn this joke at six years old in our Christmas crackers. Any other pronunciation is therefore doomed, or at least turned into an exotic curiosity, in our childhood.
*Please feel free to introduce me to the art of phonetics. I'm curious.
Traditionally, when learning Latin, one is taught to pronounce a trailing 'i' such as that in Gemini as "ee." So if you want to hew closer to the classical pronunciation of such words, such as the Oracle of Delphi, go with the "ee." (Warning: In US English, this will generally sound astoundingly pedantic and pompous.)
Up until the sixteenth century, English scholars pronounced their Latin '-i' the same way as everybody else did, viz /i:/ ('-ee', if you will).
But when the English long vowels made their great trek around the mouth over the next two centuries, they took the Latin vowels with them on the trip.
So between then and the early 20th Century, in most contexts English scholars (and lawyers) pronounced Latin words more or less as if they were English, hence bizarreries like "Decree nisi" (/naɪsaɪ/).
Some time in the 20th century, classicists realised what had happened, and endeavoured to return Latin (and Greek) scholarship to something very much closer to how the classical languages had actually been pronounced. This didn't have much effect Latin words that had entered English - except when it did.
The consequence is that there is confusion between /i:/ and /aɪ/ for '-i', and between /aɪ/ and /i:/ for '-ae'. Go figure.