Najlepszą bronią przeciw wrogowi jest inny wróg.

English Translation

The best weapon against an enemy is another enemy.

The concept of using the instrumental when using the verb “być” has to be the concept I struggle with the most. Can anyone explain to me the difference between:

“najlepszą bronią” paired with “inny wróg”
vs
“najlepsza broń” paired with “innym wrogiem”

Just when I think that I got how this works, and what effect using the instrumental on one side or the other relative to być makes, I lose track of things.

English language doesn’t have dopełniacz or mianownik, so swapping subject and object is impossible in the English sentence: The best weapon against the enemy is another enemy.

The Polish sentence Inny wróg jest najlepszą bronią przeciw wrogowi makes perfect, identical sense although not being as natural, whereas Najlepsza broń przeciw wrogowi jest innym wrogiem means that the weapon is our enemy, which doesn’t make any sense and therefore cannot be even translated. Note though that the second sentence is also grammatically correct.

That’s precisely what I’m really struggling with. Why is the second sentence less natural, even if it’s still gramatically correct? What is the actual implication of swapping the instrumental between najlepsza broń and inny wróg? When I was starting to learn polish, I was introduced to the instrumental case through Duolingo with phrases such as “Tygrys jest kotem”, and in such examples it was easy for me to discern one side from the other, because only one variation is true.

You say that " Najlepsza broń przeciw wrogowi jest innym wrogiem means that the weapon is our enemy, which doesn’t make any sense and therefore cannot be even translated." but this is not what the sentence is. The sentence is saying the weapon is another enemy, so in the end, I still don’t see how one variaton makes sense, and the other doesn’t.

Sorry if I’m being annoying with this, but I feel like this might be the thing that unlocks this in my mind.

Let’s look at a simpler example: Kwadrat jest prostokątem (A square is a rectangle). Here Kwadrat is mianownik and prostokątem is narzędnik.

Natural construction: mianownik + jest + narzędnik
Less natural construction: narzędnik + jest + mianownik (prostokątem jest kwadrat)

The relation between mianownik and narzędnik suggests that every mianownik is a narzędnik (every square is a rectangle), but not the other way around. Hope it helps.

Polish jest isn’t exactly what English is is. If you want to exactly translate is into Polish, you should use a construction like jest tym samym, co or to: Broń to inny wróg. From Orwell’s 1984, Wojna to pokój. Wolność to niewola. Ignorancja to siła. (War is peace. Freedom is slavery. Ignorance is strength.) Translating it as wojna jest pokojem would be completely incorrect and would change the meaning.