Yup, good reason. Character was only abusive to eldest daughter, which is why abandoning her was a good thing. She wasn’t abusive to second daughter but, in the long run, it was a good thing that daughter was also abandoned because who knows what could’ve happened there
In January, February, March, the eldest brother of the main character was in a prophecy.
Basically the prophecy stated that the brother could destroy the planet after a certain point.
The mother was all for killing him to protect the other kids, but the father convinced her to abandon him, so they did, before the main character or his younger siblings were even born (they had three kids at the point of when the eldest brother was abandoned).
So as a bit of back-ground info, in this particular world (Panavora) it’s widely believed that not all children are born equal, some are born with sin. This stems from the idea that “nothing good can come from evil” therefore, if the act to create a child was evil, that child would in turn be evil (or to be more precise, reflect sin). These people were called “bastia”.
The MC is a bastia. The emperor was married with a child on the way when he had an affair with the MC’s mother. By law, all bastia must be claimed legally by their parents (and somewhat provided for), but overall bastia are seen as incredibly embarrassing. A blemish on an otherwise perfect reputation, and someone who a lot of people want to ignore (especially if they’re important politically).
With this in mind, the emperor “legitimized” her as his child, and then sent her to live with her maternal grandmother. At this point, her father didn’t really see her as a person. More a mistake, and he entrusted the maternal grandmother (who was very religious) to basically hide the MC away from the world.
He didn’t meet her until she was eleven after maternal grandmother died, and soon thereafter sent her to a military academy, lol.
Her mother is a bit more complicated, but to cut things short as this is getting too long, absolutely psychologically distressed and with her purpose, outlook, reputation, etc. all obliterated due to conceiving a child, her mother had a psychotic breakdown. Afterwards, she convinced the emperor to save her, and he agreed to make her a concubine (not an easy thing to do) so long as she agree to have limited contact with the MC as to improve her public image, and to maintain loyal to him. She agreed. This is extra shitty because the MC’s mother (the maternal grandmother) was the WORST candidate to take care of the MC, and the mother left her there with little to no thought for her well-being.
Overall, and basically, the MC was only ever seen as an object and was never humanized by her parents, who considered and saw her as a mistake (and the culmination of their sin) forever there to represent their dark desires. Which feeds into the idea of her character–a human who was not allowed to ever feel like one.