"Why would Apple care about headphone compatibility with Android?"
I have a pair of reasonable headphones. They're about £30. I use them with my phone for music. My PC for music. My iPad for my German learning. I'm not an audiophile, but I find that's the price to get a decent sound. If you're forcing me to have a different jack, it doesn't just mean I've got to carry 2 pairs of headphones around, it also means that I have to buy another pair of headphones (which will be over £30, I'm sure). It means that anyone currently on Android, or who has spent out on good headphones with their iPhone has a new charge for iPhone upgrades, and it's another reason to switch to Android.
And personally, I don't understand this fascination with making phones thinner. I'd rather have a slightly thicker phone and more battery life.