Do I have to break up?

I am in a committed relationship. We both love each other a lot. I am more of a conservative type. He is of free spirit. He does casual flirting and in the past he used to have intimate talk with a friend on phone. I knew about her. That was long back when I was not in his life. Recently she contacted him and they both had some professional discussions. I know it was mainly professional. But during the discussion (I saw this in their chat) out of blue when he asked her what is she doing. She replied i am bathing. He asked her are you naked in bathroom right now? She said yes. He asked her do you remember me?. She said yes. Then he asked her i want the proof otherwise i don't believe. That's it. He then said her sorry it was a joke. Even she was very casual about it because they had history. But i am very deeply hurt with this. I couldn't digest it. He says it was friendly banter. There is no emotional attachment or feelings involved there. He accepted it was a mistake to talk like that but he had no sexual intentions. The talk was out of blue, a joke and friendly teasing. I don't know what to do. I know he doesn't cheat me and loves me. But the conversation hurt me deeply and i asked for break up. He pleaded me there is nothing between her and me. Since he talked to her after many days and during the whole discussion he was only trying to tease her. Please help me. I love this person. I need advice what to do now.