Nozel looked down at Noelle, as he threw all her belongings outside the mansion

"You don't belong in the House of Silva! You're nothing but a failure!"

You stopped Nozel from hitting Noelle as you say; "Onii-sama! Please don't hurt my twin!"

Nozel: And you too! You don't belong here in our mansion nor in the Silver Eagles!

He threw you out as well as your belongings, and that's how you became a member of Black Bulls.