Make room for the other version
Ask what the other person understood before assuming that you are arguing about the same facts. For a message about how to apologize for missing a friend's celebration, use this factual base: identify the moment, the impact on trust or inclusion, and what your friend should not have had to carry.
Correct the record precisely
Correct only what you can support, acknowledge any real impact, and propose a practical way to prevent repetition. Offer a repair that matches the harm and show how your behavior will be different. Make the immediate next step clear enough that the recipient can answer without reconstructing the entire history.
Agree on a testable next step
Do not use shared history, mutual friends, or public gestures to pressure a private response. If contact is unwelcome, stop and avoid using mutual friends as messengers. Do not recruit an audience, publish private evidence, or turn a misunderstanding into a campaign about character.