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.
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Saying that someone else "makes us feel" an emotion suggests that they are responsible for our emotional state, and that's highly problematic.
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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.