알지도 못하는 것들이 감히 아버지 앞에서 가들가들 가르치려 든다 --> To patronize (어감: 우수하는 느낌)
영어로는 I dared to patronize my father with things he didn't know 뜻이 된다.
A very common expression --> "Don't patronize me" --> don't act superior to me.
원래 그는 한국에 왔을 때 꽤 거들먹거린다 --> To condescend/ To be condescending to someone (어감: 오만하는 느낌)
영어로는 When he first came to Korea, he was quite condescending/ arrogant 뜻이 된다.
A very common expression --> "When you speak, don't be condescending" --> Don't be arrogant in front of someone
arrogance --> Even though you know, you don't care. 알아도 상관이 없다
Ignorant --> because you haven't been informed, you don't know. 알리지 않아서 모르다.
Hope this helps.