Not "uncaring" but have seen so much of it that you learn to approach it differently.
Just like some people faint at the sight of a little blood and a paramedic has seen so much of it that even when there's gallons on the floor he/she calmly goes about assessing the situation and dealing with what needs to be done.
Aside from all the deaths in my family/friends, I spent 15+ years dealing with auto accident lawsuits, lots of dead bodies and, unlike my family, not doing so serenely in their own beds. I've seen accident photos where you absolutely have to shut down any shred of emotion to be able to deal with the task at hand. Some people couldn't, and refugeed to nice clean (boring) fields like tax law and contracts.
I care that there are problems in the world, but I also know that it's beyond my power to fix them, and pointless for me to lie awake at night worrying about things I can't change. I learned long ago that I can't help the whole world, I have to concern myself with making my little corner of the world a better place. My personal resources are spread too thin just dealing with people I actually know who are dying of incurable diseases; that doesn't mean I don't care about dead babies in Africa, just that there are things I can fix and people whose hands I can hold F2F who are a higher priority for my limited resources. I've delegated the problems in Africa to my cousin the medical missionary and to Bill Gates' charity, and they have delegated caring for my personal friends to me.