Under what kinds of circumstances do you say or hear, "this isn't about you," or "this isn't about me"?

In the psychology books, it seems like there’s this thing about owning your own feelings, or not depending on someone else to make you feel one way or another, or about dealing with your feelings on your own. I guess if my spouse gets angry with me, supposedly it’s not about what I did, but about her reaction to it?

I guess this lets you off the hook? You’re not responsible for how someone else feels? But if they’re angry with you, surely they will do something to make you feel the consequences? Are you supposed to do nothing when someone is angry with you?

If you don’t care what the other person feels because it is their feeling, not your responsibility, isn’t that a recipe for disaster? The other person will feel like you don’t really care, and the relationship will probably end.

I probably have that wrong, so can you guys help? Can you give examples of when you’ve said these phrases and why you said them in those circumstances?