When I'm on FaceTime with my friend and we both want to listen to music, how come if I turn on my music on iTunes, the person I'm facetiming with can't hear it?
To prevent audio feedback, FaceTime will try to cancel any audio the mic picks up that is coming from the same device's speaker. For your friend to hear your music, play it from a different device than the one you are using for FaceTime.
It seems to occur in many iPhone and iPad models. in FaceTime call, OS will lower the playback volume of your music, and send it only to the headphones connected to the phone.