I agree with the other commenter that woefully, Latin is a dead language. The author lists examples of modern usage of Latin in the article that, imo, are few and far between. They almost always resort to neologisms and English back ports on the spot, or reuse some Latin vocabulary that hopefully makes sense. In the manned mission to Mars video by Paideia the author linked, the speaker rather handwavily refers to the rovers Opportunity and Curiosity as instrumenta, while his slides uses carri (wagons). I don’t think there is any consensus on what rovers should be called. Articles on the Latin Wikipedia (that the author also links to) painstakingly avoids this issue by de-Anglicizing official NASA monikers (so Curiosity is Laboratorium Scientificum Martianum, or just vehiculum).
I’m not saying the way modern Latin creates new vocabulary is bad--most non-English languages have gone through a similar process. I am lamenting the absolute lack of consistency or consensus, because the corpus is so small and because Latin speakers rarely actually communicate in Latin about such matters for practical ends. The Maritian mission lecture can uncharitably be said to be a mediocre high school presentation on the subject, with the novelty of it being in Latin (and again, I like Latin as a language a lot. I almost went on a Paideia trip before their scandal cropped up). And yes, novelty is the biggest factor here--why are all the numbers in Roman numerals? Cultures around the world have adopted to Arabic numerals despite all having indigenous systems.
I am aware that the Latinitas Foundation publises a Lexicon Recentis Latinitatis, and you can see a small portion of it on the Vatican website: https://www.vatican.va/roman_curia/institutions_connected/la.... The problem is that it simply has lemma in Italian and Latin explanations to them, which is not exactly helpful (or sometimes correct). “Jet” is explained as aërināvis celérrima (the fastest airship) and “jumbo” as capacíssima aërināvis (the largest airship; wouldn’t it be prudent to think it might refer to things other than a plane?). Also I am under the impression that planes are more often referred to as aeroplanum, because loaning from English gets more traction (like computatrum vs ordinatrum). It’s ironic that in the information age, when dialects in living languages are increasingly homogenized, Latin is so fragmented—-again, probably because people don’t actually communicate in it. Remind me how Latin got replaced by the veraculars?
This is becoming a huge rant, but as someone who has experience teaching myself language to fairly high levels, an excess of engaging learning materials is crucial for achiving proficiency. Imagine learning English and you get to choose from the huge and diverse corpus of Shakespeare, Milton, Samuel Richardson, Shelly and Dickens. Not that any of those is not a great work, but to achieve listening and speaking skills, you obviously need other materials: news, pop culture, entertainment, instruction manuals, random people’s posts online–the equivalents to which Latin cannot provide. If you are trained to read and analyze only the classics, you will be able to do that--maybe you can't listen or speak or sight read, but what did you really expect.
That said, I do not regret not having been part of a “living” kind of Latin language course. Language instruction in the US is atrocious, and I learned nothing from 3 years of French courses despite good grades. Grammar-translation might not be ideal (I didn’t do it for long either), but at least it has rigor.
Secondly, you are wrong in that Latin is a dead language. A surprising number of people speak it actively and Latin is still the main official language of the Holy See. They even publish a Latin dictionary with modern vocabulary that contains words like smog, gangster, radar, telenovela and hand grenade ("Lexicon recentis Latinitatis"). There are other modern Latin dictionaries available online as well.
There is a chance that your "bicycle" word came from that dictionary and your teacher just didn't know that.
These words are no less made up than the word "computer" is made up in the English language (of course, computer also comes from Latin, "computare", to count). I mean, someone called it that or in some countries groups of linguists come to the opinion that this is what a thing should be called, and voilà, you have a new word. Why shouldn't that happen in Latin?
Latin also was an official language in Hungary, Croatia and Poland until the mid 19th century, so it wouldn't be a surprise to find some fairly modern vocabulary in it as well.
As for the usefulness of Latin today, even if you're not in the Vatican or speak it for fun: It does give you a surprising leg up in learning Italian, French, Spanish, Portuguese, English and basically all technical terms found in the fields of medicine, botany and many more. About 60 percent of English words are borrowed from Latin (or Greek), in scientific or technological areas this number rises to more than 90 percent. About 10 percent of words are purely Latin, the rest found their way into English via French and other influences. Of course that helps you both ways... you will be able to recognize many Latin words without much effort and this can make learning Latin a lot of fun!
That's for the vocabulary only.
As far as what you can read when you study Latin: It opens a whole new world of thought, history, philosophy etc. for you. You will find that in many ways, there where very insightful (and arguably more mature) ways of thinking about things some 2000 years ago. You will also find, to your amusement, that there are several quite popular "self-help books" on the market today which are just badly ripped off versions of ancient Latin texts...
Latin is quite possibly the only language that played a major global role for thousands of years continuously (until maybe the 18th/19th century). That means something. Of course you can read much (but not all) of it in translation (not many people bother, however).
I encourage you, if you're keen, to pick up a better Latin textbook than the one that caused you so much frustration and anger towards Latin. Check out "Lingua latina per se illustrata" for example, which is a simple, amazing book that you will be able to read without doing any translation or learning grammar (much like immersion). Try to translate the title I just mentioned, I'm sure you can understand every single word of it even without knowing any Latin! Well, now you do know some Latin! ;-) It's fun, I highly recommend it.