One really interesting aspect of empathy is that it seems to have evolved as a pain avoidance tool - you see someone else burn their hand, see them react by saying "Ouch!", and you feel a shadow of the pain they're in, and don't make the same mistake. When we feel too much empathy for people - e.g. someone we're close to is in pain - often people give advice that is selfish - you're in pain, and it's hurting me, so while I want to help, what I'm really doing is trying to minimize my own suffering by (often inadvertently) minimizing yours. Helping other people is hard, both because we often don't know what to do, and because even our best intentions can get distorted by our ape brains.

And to be clear, the advice in the comic is bad advice when it's given in those contexts. For good advice that's shaped kind of the same way, I'd suggest reading "Peace is Every Step" by Thich Naht Hanh - lmk and I can send you a copy (It's on libgen). Alternatively, reading the stoics (as someone else suggested in this thread) would be a good place to start.