I'm going to encourage my gf to leave her family
Why do you want your girlfriend to leave her family?
I will be there for her no matter what, she is the only one I care for.
It is great that you are planning on supporting your partner no matter what. It is very difficult however to break away from family. Her family will always be her family, and even if she breaks away from them at some point they will be back.
So are you saying that I should not encourage my gf to leave her family?
It's wrong to encourage your girlfriend to leave her family. Your girlfriend needs a bigger support circle than just you. It would be innappropriate and controlling to suggest that you are the only person that she should have in her life.