Since you stated that you are cured, it means that you don’t have hepatitis C anymore, so there is no virus to pass. Hepatitis C antibodies are evidence that you had hepatitis C at some point in your life and your immune system responded to it. They exist whether you are cured or not.
Perhaps this analogy will help. Imagine you ate a special meal and just before devouring it, you took a snapshot of it. Later, you saw the photo and remembered the occasion. The picture shows the meal you once had, but you can’t share that experience with anyone else because a picture of food is not food. Loosely speaking, antibodies are like a snapshot of a virus, but they aren’t the actual virus.