There are a number of reasons for this:-
1. I am morbid
2. I see dead people (real ones)
3. I love people, I worry about them dying
4. I have some non-descript higher function
How do we know we are going to die? I suppose by extrapolation we see him die, and him, and her, and them and sooner or later you are told you are going to and it just becomes a truth, the only inevitable thing.
Take a swan, if you see ten swans that are all white, some would say thats enough, swans are white. Perhaps you need more convincing, perhaps you need to see a hundred or a thousand white swans to say swans are white. The only problem with saying that swans are white is that the next one might be black. You haven't seen all the swans. Perhaps it's a fundamental, but necessary, flaw of the mind to extrapolate.
Why do we need to? Well I suppose chiefly to learn. You can't discover everything that is known now again, you have to accept a theory to add to it (an ability I've been told I lack). We are inherently accepting, and it takes an awful lot of effort to resist it and think.
All I'm saying is just because they died, doesn't mean I'm going to.