Just a couple days ago, thinking about my cat that I had to put down ~6 months ago. He was sick and in pain but I'm still sad about it.

I don't think you need to push yourself to cry. Everyone processes their emotions differently. For a long time I also didn't cry much/at all. I was very guarded about my emotions. Between getting older and my wife, whom I can be completely open with, I have gotten more emotional as I have gotten older.