Is it normal to not care about your friends or family?

I think I'll start off by making some things clear: I know I'm not psychopathic, sociopathic, or truly antisocial. I just want to know how many other people feel similarly towards their friends and family, and if my behavior is distasteful to the more emotionally ept population.

I had a recent spat with my friend, ending with her accusing me of not caring about her. Instead of being offended, I actually thought her words rang a bit true. It's not as if I hate her. Sure, I find her annoying, but I can objectively see that she's a good person. I just wouldn't be all too bothered if she died in a car accident or committed suicide or anything. I know she has chronic depression, too, so the whole suicide thing is an actual possibility. She even told me she tried to kill herself with pills, once. It didn't really have much affect on me—in fact, I thought it was kind of pathetic.

And it's not just her. I find it hard to care about anyone, really. My sister, my brother, my father, my mother. They just don't matter to me. Even another one of my friends, probably the only person who would really understand my feelings about others, doesn't matter to me. He doesn't plan on sticking around for very long, and I know I'll miss him, but I also know I won't cry over him.

My grandma is getting up there in age, and I'm sure these next few years are going to be her last. My family didn't find my reaction to our cat's death to stellar, so Gram Gram's funeral should be a real treat.

So, in a nutshell, I'm asking you all if it's normal to not care about your friends' and family's happiness, depression, health, well-being, or deaths.