Oh, this is horseshit. Dad knew that Tarou's grandfather had seen first love zombies for DECADES and he's still alive even after seeing them again. So this "IMMA SAVE MY SON... ALSO PLEASE IGNORE THAT I'VE BEEN TRYING TO STEAL THIS POWER FROM TAROU AND DESPERATELY WANT IT BECAUSE I'M A PERVERT/LEECHER" reasoning is self-serving and an excuse. He knows Tarou isn't going to die from this (IRONICALLY he's more likely to die from whatever bullshit stunt his father has been pulling - this is perhaps the most taxing and harmful we've seen of the exertion put onto Tarou yet) alone.
Also, plot is... a fucking mess. It's like the mangaka doesn't know whether or not they should end the story and they sure as hell don't know how to end it at this point, so they're just going for the "throw twists and turns! do something!" gambit.
My only guess is that what "Dark" Eve was referring to is she'll realize that Tarou is better off without her because Tarou should have a relationship with the flesh-and-blood world and not his own hallucination and that this is causing him harm in the long run (and, no, I'm not talking about "you're going to die!" harm necessarily) and will leave Tarou willingly in order to protect him. And my guess is Eve is Tarou's link to his abilities because... plot contrivance reasons... and he'll lose his ability once she leaves. Just a guess, but that's the only thing "you'll never see him again because you won't want to" seems to point at. And the "Dark" Eve was her dark side being somewhat selfish and wanting to keep Tarou because she loves him.