Sometimes you meet someone, you get to know her, and then you don't know how to say goodbye. Why is that? Why can't I say goodbye?

Because you got attached. You got an emotional connection towards them. I felt like that when I met someone at the hospital going through similar shit to me. We never did meet again and we never did get to exchange phone numbers. We hugged. And We talked about personal stuff to a stranger. I was 15. I felt good as I met someone with similar issues. Also you might have been worried you would never see them again.