"Dlaczego nie?"

Translation: Why not?

[AidanGiord]

Is there a difference between czemu and dlaczego?

[Jellei]

Not really. But some people may find "czemu" a bit more colloquial, also some people (Hi mom!) tend to think that it is 'worse' because it's a Russicism. (cf. Russian почему)

[AidanGiord]

Thank you!

[AnCatDubh]

Does Polish distinguish between ‘as a result of what causes’ and ‘for what purpose’ like Russian does?

[immery]

I don't know Russian, but in Polish you can use Dlaczego as both
as a result of what cause= Z jakiego powodu?
for what purpose= W jakim celu ?, po co? na co?

Po co? (or more colloquial na co?) are common in spoken language

[Mira447168]

Warum nicht?)

[tczek]

Shouldn't dlaczego be genetive as it is preceded by nie therefore is a negative sentence?

[alik1989]

Dlaczego is neither a (pro-)noun, nor an adjective, nor a numeral, so it's indeclinable.