I (f25) found a text message from my boyfriend (m23) telling one of his lady friend's that he is breaking up with me and asking her out. But we were having a fight when he did. Should I be worried?

I have had some trust issues with my partners in the past. My current boyfriend is the sweetest, most fun and charming guy I've ever been with, even if he has the occasional anger issues. He does everything for me, and if anything, he complains that I don't reciprocate to the same degree (even though I try!).

However, since the beginning of our relationship over 3 years ago, there has been this girl that he tells EVERYTHING to. Naturally, me being a nervous person, this has bothered me. I have spoken to him about it many times and he has reassured me, and I drop it and leave him in peace until the next time. However, two days ago I did a bad thing and (for the first time and I'm really sorry about it) I looked through his messages with this girl. What I found was him venting to her about our relationship. She responded that maybe he should break up with me, and he responded "yes, maybe I should. I'll give her a month to change. If I do [break up with her], would you get with a guy like me?"

My question is how the hell do I respond to this? What do I say to him? What do I do about this girl?

TL;DR: my boyfriend told another girl he was breaking up with me and then essentially asked her out. However, he is wonderful in pretty much every other way. What should I do?