In the question of this being pedophilia or romance or whatever, I think that’s all a bit outside of the situation.
From what we’ve seen of demons, it doesn’t look like many, if any, are actually raised in a place with parents until they are grown. Instead, as soon as they can possibly fend for themselves, they’re tossed out on their own. Any relationships among demons so far have just shown loose networks of friends.
So it’s very possible that given how he’s one of the few sapient beings to positively interact with her in her life, she views him in more of a guardian/parent role. The fear of him getting into a relationship would make sense considering how he only fed her since he had just broken up with his girlfriend. If he gets another one, in her mind that could then flip the current situation back to before.
This could also be looking at it in a more Freudian way. Freud thought that our ideal romantic partner was our parent of the opposite sex (sons attracted to their mothers, daughters attracted to their fathers) since for many they were the first and longest-lasting relationship with a member of the opposite sex.
But I doubt that’s the story here, since he hasn’t done anything to reciprocate. And unless she suddenly wakes up one morning physically mature out of the blue, I doubt this will be anything more than an adopted daughter and father story.