Fact : a little over 150,000 people die every single day. That's about 50 times as many people that died in the 9/11 attacks. So quite frankly I just don't care when I see some news story about a school shooting that killed a couple dozen people or a 'horrible' natural disaster that takes a couple lives and destroys some homes. I'm actually quite cynical about it, to me those things are just stories that sell, something that other people can vicariously indulge in. More and more I'm starting to see humans as a whole like some kind of virus or parasite on this planet, with our cities spread around the world like giant ant colonies, constantly multiplying and consuming. I think agent smith's speeches from the matrix series encapsulates it pretty well, he was like the embodiment of existentialist apathy.
However, when it comes to the real world, the world around me, the one I experience, I think I do have a decent amount of empathy. I do care about other people, more than I care about myself in many cases. I probably wouldn't even be able to go hunting, I'd feel like crap for killing another animal. That's why I think there's two different types of empathy: general empathy and real life empathy. So just because you don't care about tragic news stories doesn't make you a horrible person in my opinion.