Would you break up if your partner is meeting and texting their ex behind your back? He refused to show me their conversations?

Anonymous
My boyfriend was dumped by this girl before we met, and when I found out I asked him to promise me no to hurt me for the sake of this girl in the future and he promised. Two years later I found out he has met her twice behind my back and when I asked him to show me how much have they been talking? And what has he been telling her? And to at least tell her about me and about us, he told he will and then he never showed a proof of it. He also refused to cut contact with her and said "We are just friends"

I broke up with him, it was not the first time he badly breaks my trust anyway. Would you have felt the same?
Would you break up if your partner is meeting and texting their ex behind your back? He refused to show me their conversations?
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