Languages are more than just encodings for meaning -- the language you think in gives you the basic units of meaning that you use to navigate the world. You can put 'untranslatable' into Google to look at lists of words to gain an intuitive understanding of what it is like to have access to another language. My quick search turned up this -
https://www.boredpanda.com/untranslatable-words-found-in-tra... - which I think gives a good impression. Reading this list, you feel the impact of useful ideas, circles drawn around things you had never quite realized were
things before, words you wish you had.
You might think it's a problem you can remedy by borrowing words from other languages until you have all the concepts. But it's not that simple. Languages are a whole ecosystem -- words, idioms, culture, ways of seeing and being, grammars -- they come together into an inimitable whole. The whole system is like those words; if you cannot have it, you lose ways of seeing the world.
Borrowing words still loses things -- it loses connections and connotations. Maybe I don't need the German "handschuh" (hand-shoe) because I have "glove", but I gain something by the perspective even if the literal meaning is the same. A favorite word of mine from ancient Greek is apo-kara-dokia -- it means eager, expectant watchfulness, that feeling the moment the lights go low and the movie is about to start, but sustained and persistent, like watching the tunnel at the airport waiting for someone you love to arrive, waiting and knowing they will. Like "handshoe", it has a literal breakdown -- "watching from the head" -- that captures those wide eyes and forward leaning alertness in the moment. English has "anticipation" or any number of shabby substitutes, but there's no competing with the Greek.
You can't just add onto vocabulary endlessly in one language. English doesn't have 'handshoes' precisely because it does have 'gloves', and it doesn't have 'watching-from-the-head' precisely because it does have anticipation. Words die out if you don't use them, and you lose whole ways of seeing the world.
Another thing you lose is when one word has two meanings, but they're really sort of related. For example, ancient Greek 'pharmacon' means "drugs" (like pharmacy), but it also means "sorcery", and I very much enjoy the connection that those are sort of subjectively similar things. The more expansive concept doesn't have an equivalent in English, and I'm the poorer for it -- but the richer for another language having taught me to see things that way.
It's easy to explain with words. It's harder to explain with grammar. But you encounter the same phenomenon. Some languages have tenses and cases with more precise or less precise or just different meanings that the ones you grew up with -- and like the different words drawing bigger or smaller or just different circles around concepts, they give you another window into thinking about the world.
But it all works together. The breaking-down-and-constructing aspect of German as a language is related to the way Germans are given to engineering, and the way German philosophers approach the world. If you encounter them in something other than their native language, you miss something of the whole. Translators will sometimes borrow words to try to fill the gap, but it's a poor substitute. Likewise, the logical precision and colorful concepts of ancient Greek inform the way its epic poets and ancient philosophers moved through the world -- and again, they are poorer in translation.
Even idioms enrichen. The Chinese "Heaven is high and the emperor is far away" - https://en.wikipedia.org/wiki/Heaven_is_high_and_the_emperor... -- is so very Chinese in experience, and the fact that the Chinese saying itself is a pithy four words makes it work all the better in the context in which it is apropos. If we lost the Chinese language and its experience and culture, perhaps we could still say literally the same thing, but could not say quite exactly this, not with all its force of experience and history and character. And we would be poorer.
Languages and cultures and philosophies and histories and environments all feed back on each other, and they are this phenomenon of creating ways of seeing things, happening over and over in many contexts, building into a cohesive whole. This is why they are valuable to study and valuable to preserve.