Hmm for the second part, i feel like the father really cares and loves her daughter its just that he's really cold and not very affectionate before. But now with the ml interaction, its kinda changing and now the father is showing his emotions.
from what i observe from chaps is that the ml was there before she died and he was like stopping her. I think that was the time ml was checking fl in the cage bcz his teacher(the father) has a weakness. And it was the same with the ml checking the fl in her bedroom.
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Spoiler
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Okay idk abt the first or last thing but there was a spoiler thread about the dad actually planning to sneak her out of prison in her last life and giving her the dagger for self defense (?) But she misunderstood it as him wanting her to kill herself. I don't remember this part of the spoiler so clearly but i think the dad was planning the rebellion and that's why the princess died?? Idk.
But the dad wasn't really bad he was just awkward with her.
The reason he was never there was bc the emperor kept calling on him and he had to obey him so he was out a lot bc of the emperor (why he kept obeying or didn't rebel earlier idk either)
spoiler about her father
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for reasons i won’t spoil, whenever she was around her father as a child she would get severe panic attacks and her father was really hurt by this... eventually her memory gets sealed (so she no longer gets panic attacks) but her father is scared that he will trigger her so he keeps his distance

there are just so many misunderstanding In here it made wanna smack every character... like first of all.. what the hell is wrong with the ex? i thought he dont really like mc but why suddenly become kinda yandere? thats weird
second.. why the dad suddenly change? why? is it because mc clash with the ex? why now? why so sudden? he become like a new charac its weird? i thought hes that cold type.. but hes suprisingly kinda caring?
and lastly about the cat that mc remember during her childhood... is it really the crown prince? or not related at all? kinda looks similar... but so far hes the most sensible character...
they should tag this manga HUGE MISUNDERSTAND AHEAD BEWARE because im just sooo unerved with almost everyone in here... well at least mc has a reason to think like that... by the end still good so gonna stay tune for more ╮( ̄▽ ̄)╭