I think crieing in a movie always needs the movie to evoke an experience in you, to touch you. I have watched the supposingly saddest movies and didnt cry just because everybody did. I need to personalize with the movie, it needs to evoke a feeling somehow create a connection to a real experience for me, otherwise I have troubles crieing.
I regularily cry in movies, I am usually the first one to do that but then again I have to cry at the strangest of moments aswell. For example some intro movies of some science fiction movies move me and make me cry cause I've heard them so often they almost feel like family.
I dont think you are strange if you dont cry, when you should; sometimes one is just not in the mood for crieing.