A song from a band you hate
The problem with this question is that if I dislike a band, I'm probably not going to know any of their songs well enough to remember a name of any individual one. To paraphrase Dave Barry, I've caused great pain to my car radio hitting buttons to remove "Maybe I'm Amazed" from my listening space, but I don't hate Paul McCartney.
Years ago, a very musical friend confessed that he hated everything Judy Garland had ever recorded. (I know she's not a band, but bear with me.) After a bit of chat, I went home and made him a copy of Garland singing "Purple People Eater." Friend now says that he hates almost everything Garland ever recorded.
This friend comes to mind because he's one of several people who have tried to make me enjoy the band Rush. Now, I've never heard them do "Purple People Eater" so I am willing to change my mind, but none of their music does anything for me... hence my not being able to name any of their songs.