Can't delete music from iPhone 6 through iTunes

I've been trying for an hour now to delete music from my phone via iTunes. With my old iPhone, even with iOS 8, I was able to go right into my music, select an item, and delete it. Now it won't let me. What's even more confusing is that if I delete music directly from my phone and then connect back to the computer, all the music I just deleted is automatically added back. I've never had this problem with any previous iPhone.