What if Izuku has a twin? But, she is the utter complete opposite of him. She hates heroes. She hates other people. She doesn't care about the others. She hates All Might.
Pessimistic, hateful, sarcastic, confident, powerful. Unlike Izuku, she has a quirk, scratch that she has some quirks. More than one. She is a villain. She doesn't believe in the word "hero". Why? She had gone through hell. Heroes never came. They never saved her.
She hated them. More than anything. People who called themselves heroes, who said they will save those in trouble.
She was kidnapped at a young age by a sadist villain. He loves seeing her in pain. Hence, her days are full of those and torture. Every time her sanity was being tested. Her quirk being "Instant regeneration" made the villain torture even more severe.
Every day, her sanity clutched on the rope of hope and trust. She trusted them. Heroes. She believed in them. Believed that they will come for her. It was useless. At the end, she handled it on her own. Her sanity was crushed along side her hope and trust.
The tables turned. The torturer has been the tortured. She then found out her "brother", who also didn't bother to save her is in U.A. highschool. She also found out on these League of Villains. Finding out all the things they have done, made her inspired, she loved seeing others in pain. They do that, check. Second, she wants all those "heroes" dead. Check. What else could she ask?
She joined in instantly afterwards and sent a request to enter the entrance exam.