It is different reactions for different people as others have already said.
I'm probably close to Hawk's experience, when my mom passed, I did not cry at her funeral, nor when she actually passed, I did cry before however when the doctor told me she had little time left, but that's just it, you take the news and events in a different way than other people.
My girlfriend for example, recently went with me to my grandmother's funeral, and she never met her, but was crying because other people were, she's very emotional, some of us not as much, so we take our grieving in a different way.
And no, you are not a bad person because of it.