I can empathize in situations that are familiar to me, like when they're very similar to something I've experienced myself and bring about similar feelings as I experienced when I was in that situation. For example, I can empathize with someone who is being bullied or treated badly through no fault of their own, because I've been in that situation myself and know what it feels like. I can empathize with the joy someone feels over getting a pet or having a strong bond with animals, because I understand what it feels like.
I cannot empathize well in situations that I either haven't experienced myself or have very different feelings about or that don't make sense to me or even sometimes if I feel that the person is entirely to blame for it themselves. For example, before I had ever been in a relationship myself I found it hard to empathize with people who were upset over a break up, especially if it was them who broke up with the other person. I didn't get it, if they wanted to break up then why were they upset about it? Or if they were so upset about it, why the hell did they break up? After being in a relationship myself I can understand this a bit better and can sometimes empathize, but I still can't empathize when people are upset over breaking up after a short or shallow relationship for example, or over breaking up when they knew before the relationship started that it wouldn't work out.