How can I convince my friend that I did not betray his trust? (edit)

To make a long story short, my ex boyfriend who is very much still my very best friend (and I still love him dearly) believes I told one of his friends some information and I didn’t! It was said that I went to the guy myself and told him this information (that I will not post!) and he added extra stuff in. My ex then told me he was cutting me off because I betrayed him. I told him I could understand why he was upset being that I was the only person who knew this info but I was being honest when I told him I did not tell his friend anything! In fact, I don’t know how he knew. I need help on trying to get him to understand me and not try to cut me off…How can I convince my friend that I did not betray his trust?