No need to elaborately explain your side. Sometimes, the more one explains, the more it sounds like accepting blame.

I don't appreciate, the accusation. And then, walk away from the conversation.

Reminds me, of how I'd try to soothe my ex husbands fears. It's not my job, to convince others of their erroneous beliefs. Can lead a horse to water, can't make them drink.

Simplify the response. Don't accept the blame.