I'm not one to normally post; also I am new to the world of Chinese/Korean dramas; but I think a lot of the reasons why we view a female villain with more contempt compared to a male villain can be broken down into basic stereotypical factors.
1. Romanticize a bad boy / Shun a bad girl: We are a society that sees a "Bad Boy' trope as a misunderstood character who is justified in his actions no matter what. There is also something in his story arc that can make him redeemable because people demand it so, and are not shy for letting writers know that the story was lacking because of this one fact. In fact for a much as I read; which is a lot; it's rare to find a male villain that doesn't have something that can make him redeemable in the eyes of the reader. As for the "Bad Girl" trope she has no redemption. She is seen as completely misguided because of her wants and desires. This fact means these characters are often written as the type of person who is willing to do anything to get what they want and basically sets you up to dislike them from the word go.
2. Male/Female as Childhood / Best Friends who are Love Rivals: another trope we see a lot of, this one will 95% of the time show the female character being more aggressive towards her counterpart where as the male character is merely just complacent to step aside for the main leads happiness. I think this really stands out in making the feeling of contempt for Female Villains to shine. It's here where you see the most come out of the fandom. This trope also applies to arranged marriage, or distance relative story lines as well.
I could go on, but I think the two I listed above are good points already. And really what it boils down to is that female characters need more development in general. There needs to be more depth to her. What makes a Villain such a character in general is the complexity and depth the character has built into their narrative. They are a purpose despite their internal madness which makes you want to root for them. Female characters can be this way, people just have to start writing them.
1. Romanticize a bad boy / Shun a bad girl: We are a society that sees a "Bad Boy' trope as a misunderstood character who is justified in his actions no matter what. There is also something in his story arc that can make him redeemable because people demand it so, and are not shy for letting writers know that the story was lacking because of this one fact. In fact for a much as I read; which is a lot; it's rare to find a male villain that doesn't have something that can make him redeemable in the eyes of the reader. As for the "Bad Girl" trope she has no redemption. She is seen as completely misguided because of her wants and desires. This fact means these characters are often written as the type of person who is willing to do anything to get what they want and basically sets you up to dislike them from the word go.
2. Male/Female as Childhood / Best Friends who are Love Rivals: another trope we see a lot of, this one will 95% of the time show the female character being more aggressive towards her counterpart where as the male character is merely just complacent to step aside for the main leads happiness. I think this really stands out in making the feeling of contempt for Female Villains to shine. It's here where you see the most come out of the fandom. This trope also applies to arranged marriage, or distance relative story lines as well.
I could go on, but I think the two I listed above are good points already. And really what it boils down to is that female characters need more development in general. There needs to be more depth to her. What makes a Villain such a character in general is the complexity and depth the character has built into their narrative. They are a purpose despite their internal madness which makes you want to root for them. Female characters can be this way, people just have to start writing them.