What’s your thoughts on the female lead’s past?

After watching the 3rd and 4th episode I am acceding to my previous theory: her mother was sick, mental illness. In imaginary/memories of her FL is enormously scared, I would even say he is frightened to the core of her bones. There was some sentence "You're extremely special. You're my greatest CREATION." I guess the mother was consistently and unscrupulously bothering her child, she was abusing her and poisoning her mind to make her feel different than other kids, evil and cruel - until the point, she believed her mother.
At the same time, I have some sort of feeling her dad knew exactly what's going on. There is a huge possibility she was involved in her mother's death. This was the reason he tried to strangle her when she was a child,. That's why he asked her, why she is still alive and choked her during a walk around the garden in OK Hospital. "Die, you... You monster."
He called her a MONSTER, a monster that was created by his wife and mother of FL. A monster that was involved in her mother dead, a monster that made her father went crazy.

My theory, based on the castle made for FL when she was born. Both of parent love her so much, too much that her mother did not want her go outside and treat her like her precious thing ( mental illness due possesiveness). And probably her father love her mother too with the same amount possessiveness. I don't think she was abused physically. And after her mom passes away due some accident in that house, or probably killed herself, perhaps his father seen something and misunderstand that she want to kill her mother. I don't think she killed her mother, even though she could, based on her hatred to that blackmailed writer, she capable to kill, but decide not to. 

I can see it going many ways, but I really don't think Moon Young suffers from antisocial disorder. Sometimes this summaries are very misleading, to me this is the case here. From what I gathered she could be suffering from PTS caused by childhood abuse which could also trigger many unbalances in her relationship skills and behavior. To me, her parents seem very ill, her mom seemed very possessive towards her so I think she was mainly kept from developing early childhood friendships. It's also very odd to me that her dad would literally build a house in the middle of nowhere. Regarding her mom, I don't think she killed her, but I do think she locked her in after finding her dead. Maybe her dad also killed her mom? Or maybe she killed herself? I don't know, but we'll keep getting clues. But if it were her dad it would also give him a reason to try to kill his own daughter. He could be having an episode and convince himself that it was all her fault... I don't know, but it sounds like a possibility to me. 

Regarding the butterfly and Kang Tae running scene, I thought about maybe she knowing about his brother thinking it was a butterfly that killed his mom. Maybe she killed all the butterflies trying to show some kind of protection? It's rather easy to think that that was her being mentally ill as a child, but when children are not shown regular healthy love and care in early ages they have a different language and I could see that being the case here.