I'm mad at my bf because he's right
What do you think about your boyfriend right now?
He's an idiot for standing up to me like that
It sounds like you're frustrated that your boyfriend is right.  If you have admitted to yourself that he is in the right, you should just apologize to him for whatever you did instead of being mad at him.
I'm mad he stood up to me, even though he's right.
I think that the best thing for you to do is to accept that your boyfriend was right, and just be glad that you have learned from the disagreement. You don't need to be angry or sad that you were wrong about something, but  it wouldn't hurt to apologize to him for being unjustifiably angry.