Breakdown of Warum kämpft ihr nicht für das Projekt?
ihr
you (informal plural)
nicht
not
für
for
das Projekt
the project
Questions & Answers about Warum kämpft ihr nicht für das Projekt?
Why is ihr used here instead of Sie or du?
ihr is the informal plural 'you' (like 'you guys' or 'y'all'). You use it when speaking to two or more people you know well. If you were speaking to one person informally, you'd use du, and if speaking formally, you'd use Sie.
Why does das Projekt stay as das? Doesn't the preposition für change the case?
It actually is in the accusative case here! The preposition für always forces the following noun into the accusative case. However, because Projekt is a neuter noun, its accusative form (das Projekt) looks exactly the same as its basic nominative form.
Why does nicht go in the middle of the sentence instead of at the end?
In German, nicht is placed directly in front of the specific element it negates. Here, it negates the prepositional phrase für das Projekt (you are not fighting for the project), so it goes right before it.
Since the current lesson is about trotzdem (nevertheless), how would I answer this question using it?