She said it in the episode immediately following when Rudy and Nanahoshi met (well, formally met...) She sees their special bond that she doesn't understand, and knows they share secrets she's not privy to. In some ways, she worries that this bond is even stronger than the one (at the time) from her & Rudy's childhood.
She also recognizes that Nanahoshi does not love Rudeus. Which makes things even more confusing. Because the kinds of bonds / secrets they keep would make sense if they were secretly lovers. But she detects none of that.
She cannot trust or understand Nanahoshi. So the idea of adding Nanahoshi to the family naturally upsets her.
【Key Visual】
Shangri-La Frontier Season 3 is scheduled to premiere on January 10, 2027, and will run for two consecutive cours.
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One thing the anime doesn’t do a very good job of conveying is that Rudeus has already been at the Chaos Breaker fortress for more than a week.
The reason Rudeus asks Sylphie to go back home is because they don’t know how long it will take them to find Kishirika. If they even manage to find her, it could take months or even years, so it would be better if Lucy didn’t grow up without both of her parents. The novel implies that Sylphie puts on a disappointed expression. (Remember, she’s still struggling with her guilt.)
This reminds Rudeus that Sylphie grew up without her parents, since both of them died during the Teleportation Incident, and he thinks that maybe Sylphie believes children don’t need their parents to be around all the time. But he also remembers that if Rudeus grew up to be the way he is, it’s because Paul and Zenith took care of him when he was younger.
But, in part, Rudeus also didn’t want to expose Sylphie to the Demon Continent because he was afraid of losing another person he loved… Not after what happened to Paul.