Yes, you can empathize. You can almost feel what it must have been like to be in that situation. But, no, you don’t really know. Even if you went through something similar, you can never substitute experiences because contexts are not identical.
To shake it off and believe you “get it” and that the person at the other end of the table doesn’t is just presumptuous.
The only way to avoid this trap is to approach tough discussions by acknowledging that you’ll never really understand and then following that up by sharing what you understand and what you have learnt through your experiences.
The first requirement to any great conversation is humility.
(As I write this, I realize how often I fall short of this idea and just assume that I do understand.)