Man, I hope she figured out he's the first Prince.
There's a ton a reasons why she would think firing him would be better for him...
It could be that she wants to help him get closer to his family, that she thinks that his normal duties are hard enough without her work pilling onto it or even that she found out that she has feelings for him and that it complicates things...
But I hope she just got some more clues during their conversation as to who he really is.
She's pretty intelligent, albeit sometimes a bit naïve... so she might have deduced that, I think.