Michael was very hesitant to tell Rivet about the 'Cube'. After all, it was something that he got in the Antique Island. And he guessed that it was some kind of remnant from the Ancient Era.
Now, he knew that the Guild of Arcana was very much interested in all things about the Ancient Era. They were kind of like a museum, in a way. And he was afraid that if they knew about the 'Cube', they would take it away from him in order to study it for themselves.
He trusted Rivet. She wouldn't betray him like that. However, he still didn't want to give her the opportunity to shatter his trust.
On the other hand, he also wanted to get her favor. After all, he was asking for her signature medallion. And Aetrox warned him that getting a medallion was no simple matter.
