@Kevadu I wrote about this a few chapters ago. The only reasoning for such drastic different treatment for twins would be if they completely wrote off one from the beginning. We know now that our mc isn't naturally gloomy, just a little love made her light up like a lightbulb. So she must have been neglected by her parents from the start to make her so gloomy in the first chapter.
The parents were probably not so well off financially and were only expecting one kid. Having two mouth to feed, they probably just picked at random which child to properly care for and which one to treat as extra baggage. The o my reason they wouldn't have killed her at birth would be insurance in case the other child died from illness or something as many kids did on that time period.
Though I'm probably giving too much credit and thought to something that was probably just a plot point created for drama.