Hello there !
Correct me if I am wrong but I believe the context sentence for 粋, or rather its translation, is wrong
自分で粋な会話をしてるって思ってるところがムカツクんだよね。was translated “He believes that he carries on refined conversations, but they’re actually irritating.”
However, since what the person finds irritating in the sentence is ところ (which stands here for a characteristic of someone), I believe “The fact that he believes he carries on refined conversations is irritating”, or less literally, “It’s irritating how he thinks he carries on refined conversations”, would be more appropriate right ? (I am not english, so if you want to provide a better translation, you’re welcome )