You were being abused. You couldn't take it anymore. But you also couldn't leave your kitten, Millie. So you gently put her in your backpack and got going.
Your father wasn't looking. He was drunk, anyways. He probably didn't even notice the window in your room being opened. You made sure to lock your door before you left, then you decided to go for it. Millie was being quiet. She most likely understood what was happening. You were running away.