Second, sincerely apologize and explain the cause, process and result of your mistake.
Sister, I was wrong. I shouldn't misunderstand you just because of my subjective judgment. I understand that misunderstanding is actually the product of distrust. I shouldn't have distrusted you. Please forgive me this time. I promise I will listen to your explanation next time. If you still won't forgive me, I will always apologize to you until you are not angry. Maybe you don't listen to me now, so let's see what I do in the future. Sister, I'm not really good at communicating with people. I'm really sorry if I hurt you. Please forgive me as soon as possible and let me get rid of the days when you ignore me as soon as possible! Because it is really painful.
Love your brother.