I feel bad because of my own experiences.

When I was a kid, my parents used to always rescue old dogs from the pound. Because we didn't feel like a senior dog should be at the pound (no dog that is, but we wanted the old dogs that weren't going to be adopted to have a nice final home). We went through about 6 dogs doing that. They'd last about 3 months to a year. My parents stopped when they found out that my words to my friend calling me to say her dog died was "okay". I was 12.
The thing is I've been around death so much, pets, family, friends, acquaintances, that it doesn't faze me. Whenever someone says anything about death or related, my response is always "oh" or "I'm sorry" but my words are so hollow. And I feel bad. Because I'm usually the most empathic person, but with this, something so horrible I don't feel a damn thing. I don't regret or hate that my parents used to adopted old dogs. In fact, I loved it. Because I knew that they were getting a good home where they would be loved and cared for instead of getting euthanized or spend lonely days for the rest of their time. But I just wish it didn't numb me to death.
I've had people say "well imagine it's your family or someone you care about, wouldn't you feel bad?" Well yes of course I would. But I wouldn't dwell on it either. Be sad, get depressed here and there, move on. I've been around it so much that I know it's unavoidable. That it just happens. I just wish, I wish I had more empathy, more feelings, in my voice. Instead of it being empty when someone tells me what's going on...cause it makes me feel like shit. And I end up telling people that I'm not the person to talk to about that stuff...