This sentence gave me an epiphany, about how the genitive case implies posession. I might have tried to translate this phrase from English by looking for a word for 'of' [I am the son of this woman], but seeing this lead to something clicking in my brain.
The genitive=posession thing also helps explain why verbs like potrzebować require the genitive - if you need something, you are are implying a desire to posses. Not sure it explains why you need it for negations though.
"słucham" takes Genitive (słucham mamy), but "słyszę" takes Accusative (słyszę mamę).
"chcieć" behaves in a weird way, when you want something tangible (I want a car) it takes Accusative (Chcę samochód), but if you want something abstract (I want friendship) it takes Genitive (Chcę przyjaźni).
I think that's a common mistake, even for native speakers. Look at the declension table for https://en.wiktionary.org/wiki/ta#Polish
tą is for instrumental singular, but this phrase is in genitive, so it is tej. I have seen people talking about this mistake in other discussions, maybe someone else will comment with more info.