So I was watching a youtube video and the Youtuber kept on saying curse words and my parents heard it. I kept on watching because the video was entertaining and really didn't pay attention but my parents told me that listening to any curse words regardless of the usage is haram. So can anyone explain to me if it's haram or not?
You're being too literal.
If, say, you are watching a film about gangsters, and they swear. Then that's in character - for them - and it's not haram.
Secondly, listening is a passive and not active act. You have no control over your environment and who may, or may not swear in your hearing distance.
Swearing, as an active act, is haram. It's against al-'Ird, the dignity and honour of a Muslim.