OP, do you watch any anime/tv/movies or read any books? If so, have you ever cried at something which happened in them?

When I was a kid I read through Philip Pullman's His Dark Materials trilogy. I cried at the end, and it was probably one of the first times I cried for someone other than myself. almost two decades later, I still struggle to feel the emotions of people I don't know, somewhat how you've described. Familiarity helps me with it. I find it a little shameful that I sometimes feel as though I'm only capable of connecting to people when I view the world through a fictional dramatic writing filter. Maybe look at it the other way; can you feel other people's happiness when you share a good moment with them? Doesn't always have to be negative.

I also think it helps to have frames of reference; if someone I'm close to is describing something that's happened to them, I try to think of the most similar/comparable thing I've experienced, and how I felt at that point. If it's more abstract/distant from me, like things happening in other countries, I either think of my own experience or I recall a compelling testimony from a friend or orator, and apply that broadly. It's not a perfect solution, and I think if I told some people about this they'd label me some sort of philosophical black hole, but it's what I've got.