This process starts with an awareness that we are not an emotion, we are having an emotion. The emotion is a transitory state of mind and body, not an identity. It can feel stilted and silly to say "I'm having the experience of anger" rather than "I'm angry!" But we're well-served by heightening our awareness of the distinction between the two. Perhaps "I'm feeling angry" is a reasonable compromise.
Saying that someone else "makes us feel" an emotion suggests that they are responsible for our emotional state, and that's highly problematic.
Having established some distance between our sense of self and our subjective emotional experience, we can then assess the steps through which we have contributed to our own response.