Is it normal to not care when someone dies?

I know how you feel. Sometimes I want to grieve and wish I could cry and what not but it won't happen. It's nothing you can just get over though. A death is a permanent thing and so is the coping process. Usually, tears and extreme grief won't hit you until you realize the impact that it has on your life. For example, when my dog died, I was numb for a few days. I loved that dog but for some reason I felt no emotion. However, when we got our new puppy, that's when my tears started to flow. Seeing a new puppy instead of my old dog forced me to realize that my old dog was dead and I was immediately devastated. It took me a couple of weeks to begin accepting our new puppy.