It seems like a very strange phrase, self-empathy. Empathy is when you connect with someone's feelings or share their mental state. You, well... are yourself. How could you not experience self-empathy?
The problem is that we aren't only one self. Our future feelings aren't feelings: they're predictions. Our past feelings aren't feelings: they're memories. Who we are changes over time, and our mental state changes with mood, environment and situation. It's a little surprising that this adds up to any kind of self at all.
To connect with feelings that you don't feel right now is a particular skill. It's a skill you exercise when you decide whether to go to a party based on how you'll feel when you get there, or when you decide to relax or push yourself based on how you'll respond. It's also the skill you use to explain yourself to people, not as the you that you experience, but as the you that they experience.
Developing self-empathy takes a certain amount of distance. Understanding your feelings from the inside makes sense in the moment, but won't work later. You have to analyse those feelings while you're experiencing them to keep understanding even as your mental state changes.
On the other hand, it also requires kindness. It's sometimes tempting to believe that your past self was acting incomprehensibly because the emotions that made sense of their behaviour are gone. To develop self-empathy, you have to believe that your feelings were real, even when the only evidence is analysis that no longer feels true.