Exactly this. She told him that it is a secret when he asked, and only said that she will send him away to where he needs to go. She mentioned that there is a purpose, but she never explained that this purpose is to save the world, so Ren simply took it as him leaving her side once she finds out. See Chapter 26
You reminded me of chapter 26, thanks! Yeah the whole chapter sums up why he wouldn't be willing to tell her, even if he wants to give his everything to her and be truthful. If tell her he is the one she is looking for and she will lead him to his 'destiny' but at the cost of parting ways with her? Definitely not. Even then, the way she worded it , is as if she and him will never see each other again once she leads him to the 'destiny', which makes him even more hesitant to tell her
also, I can't help but be forgiving of Ren lmao.
I can't rlly rmbr if Vivian explicitly told Ren that she is finding him because of a world ending crisis, and even if she did he may thought of it in a joking manner or something not like that.
Maybe in Ren pov, he knows Vivian is looking for him for some reason , with the only feature she knows is that he has shadow magic and is handsome, but he doesn't know what will happen after. He wants to stay by her side, but if she found him, will she push him away? Bring him somewhere and leave him there? He's perfectly content being her househusband lmfao, so even if he has to becoming the leader of a info guild be to hide his tracks he'll do it(hmm, iirc he also scolds himself for touching her, as if he touched something holy he wasn't supposed to touch).
(And it started from since she saved him and wasn't able to bring it up after so long). He just became a coward at some point for hiding so long, cause he doesn't want her to push him away (which did happen lmao and now he is her to ask for forgiveness).