I'm obviously not normal either. I'm not going to say caring about others is something that normal people naturally do though
I think caring about others starts within ourselves relative to our early years of life. Caring for others is a learned thing. Being an active alcoholic from age 12 to age 24 didn't mean I stopped caring about others. What happened is I stop caring about myself, and because of my uncaring for myself I had little left to care about others so in effect I didn't care about others like I do today being all sober and so on and whatever.
I think it being about ourselves first is a normal human condition. I think caring about others is something more advanced than what we are born with "normally"