That's not a courtesy Nagi wants extended to begin with. She's done all she could to conceal herself from him and only show him the dead fish persona, even when he constantly tried to pry her for more when not taken in by her allure. That he comes to understand that there's more to her deep down, and that she might want him to notice that, goes against every action she has consciously undertaken, and is contradicted by the actions she unconsciously undertakes here and there. That Reiji doesn't want to be the cause of Nagi's death, if he views her as a person and not a living corpse, is against what Nagi tried to instill in him, for the most part, because she doesn't want him to know her reasons either (for whatever reason).
So let's not act like they're not both doing this to one another. Nagi had plenty of opportunities to talk to him and open up, she just doesn't want to. Same with Reiji, who doesn't want to truly know Nagi because then he can't die with her.