I think the very existence of this recording shows that you do not have an inability to react to death. There are no rules on how outwardly sad you should be towards the death of a loved one. You say that at your Grandfather's funeral all those around you were crying whilst you were not. This means nothing in regards to your respect and love toward him. People handle grief in different ways. Some weep for the their loss, some may feel angry, others become philosophical. To try and construct a music analogy for you: does the technique of an instrumentalist's playing really matter if the resulting music is just as beautiful?

In regards to hearing of the student's father passing, many might've just given off a canned response. They might not have given it much weight in their mind, or considered the implications. In your case, it triggered a plethora of though processes and emotions which ultimately led to this. It seems like you're quite conscientious and thoughtful and in getting carried away or lost in those thoughts you're forgetting that they in themselves are the reactions.

Of course, when many people have problems reacting verbally when they hear of such news. We fear that whatever we come off may sound trite or cliche to the point of seeming uncaring and disingenuous. I think the best we can do here is not try to hard to think of what the best thing to say is, what you think the other person should here, but evaluate how you're feeling and communicate that back in an empathetic manner. lil's examples demonstrated this approach quite well, I think.

I also echo other's sentiments towards your recording, you have an easy to listen to voice and a nice style. Thanks for sharing.