Some children don't have fathers, so they invent a father in their mind so as not to feel left out.
They tell their mates at school about their father and make up stories about things they have done together.
They have messages written down that they claim their absent father sent to them.
Because the father is figment of their imagination no one ever sees him and he never talks to the child or helps him/her out of difficulties.
An invisible father exists only in the imagination.