The urge to defend yourself to someone who already decided about you is strong. Let it pass.

Wanting to set the record straight is one of the stronger pulls there is, and it is worst when the accusation is unfair, because unfairness feels like something facts should fix. A mind that has already settled does not use facts that way. It treats your defence as more material, so the conversation grows and the conclusion stays exactly where it was.

Write the whole thing out and do not send it. Leave it in your notes for a day. Usually the urge drains and what remains is a shorter version, or nothing. People who matter will decide who you are from months of behaviour.