The sentence is awkward. The only scenario where it could make sense is:
You've just realized that you have mice at home. Your know your neighbor
has a cat... So, you give your wife an idea: "We need his cat" -
Potrzebujemy jego kota (genitive)/ (Potrzebny nam jego kot (nominative)
Actually, if the sentence was ever used outside of Duolingo, it would be in passive voice (the second option). Otherwise, the verb "potrzebować" is
used with quite small number of nouns associated with basic biological or spiritual needs (not "wants"). In that sense genitive (Dopełniacz) fulfills all
the most essential human needs:
We need bread/water/money/air/love/peace/time/God (to live) - Potrzebujemy chleba/wody/pieniędzy/powietrza/czasu/Boga (by żyć)
We need ("want") other things and... people to make our lives easier, but...
they are not essential, so the verb "potrzebować" is used in passive form:
We need his cat/his car/his help/him/you - Potrzebny nam jego kot/ jego samochód/jego pomoc/(On) Jest nam potrzebny/(Ty) Jesteś nam potrzebny
Because as a general rule of thumb the allocation of words to meanings is fairly arbitrary. It works the other way around as well though ... For example: "o" in Polish = "about" in English, making the English word a whopping five times as long as the Polish, shock horror!!! :O ;)
I know you probably weren't looking for an answer. You're not alone though. I get frustrated with long words too... Polish word grammar is frustratingly specific =D
It's because „potrzebować” is one of those verbs that need direct object in genitive.
If it helps, think of it like that – you rarely state the need of something you already possess, so on conceptual level, this verb negates your possession and therefore follows the normal rule of genitive with negations. ;)
ować and awać is the most easy ending
it is always uję for ować and aję for awać
ujesz and ajesz uje and aje ujemy and ajemy ujecie and ajecie ują and ają
I have a whole tabel which includes I think 80 / 90 % of all the grammar and different cases that can occur, including nouns, conjugation, all kind of prounouns , imperativ forms, tenses. as soon as it is done i will upload it here and a native speaker can look through it.