I'm thinking of outing my brother to my mom
Have you thought about the ramifications of outing him? What will your mother say?
I think that she deserves to know who he really is.
I can tell that you feel burdened by keeping your brother's secret. You shouldn't tell your mom about a secret your brother shared with you, unless he's in danger. If you tell your mom your brother will feel betrayed.
I'm his brother and I need to stick up for him. He has done some awful things but he isn't a bad person.
I believe you, I am sure your brother is a wonderful man. But, this is his personal information to share, so even if she deserves to know, it's not your job to tell her. You should talk to your brother about this decision and he might come to the same conclusion as you and tell your mom on his own.