I've had an elderly tabby cat die of old age right in front of me, and I found my old dog dead soon after he died.
I wish I could block out the memory of my cat breathing her last breath and becoming rigid in front of me in a curled position on her side. I really wish I hadn't been looking at that precise moment.
I don't know what's more upsetting about losing a pet, the fact that a part of your family is gone, or the reminder that everything dies and we only have one brief life to live on this earth.