How do music/video mixes remain up

Hello, I'm posting on behalf of my dad. He likes to mix music and music videos, and he's uploading them to YT so that he can share his favourite music in his favourite format (a video mix). He does it for the fun of it, and isn't interested in obtaining money from them.

However, he's very confused as to how his videos remain private but others are allowed to stay up. "Copyrighted content" feels more like an umbrella term than an actual explanation, and while we know that there's no way to play the copyrighted content just like that, I'm wondering if there's a way to at least allow them to be public.

Is it the music? I've heard that the videos can be even more protected than the music. Is there a way to know which song to remove so that the video is allowed to be up?

Thanks in advance!