Interesting discovery...
Some recorded music uses stereo rather extensively: The two sound channels don't sound much alike at all. You don't notice this quite as much on speakers as you do on headphones.
Apparently, when I listen to such music on headphones, if I wear them the "right" way the music sounds slightly choppy and disorienting - but if I flip the headphones, so the right channel goes to my left ear and vice-versa, the music suddenly sounds completely natural. Apparently ear dominance is a real and easily detected thing.
Creepy.