Our Father who art in heaven
Hallowed be thy name
We give God many titles - Creator, Judge, Most Holy, etc. Why do we call God "Father"?
God did not create us en masse or just create the idea of humanity, the template for the species. He has created us personally, directly, and continues to devote specific attention to each of us. He knows "every hair" on our heads. His act of creation and His personal interest in our growth is fatherly.
As each father should be there to listen to his child's needs and wants, God listens to each of us. And like a good father, He does not always give us what we want. His attention to our wants and prudence in fulfilling them is fatherly.
A father sets down rules for the good of his children, teaches them how to obey those rules, and disciplines when necessary. God's rules, the natural moral law, are etched into each of our hearts, there to be discovered by each person that searches within for what is right and wrong. More concretely, the natural moral law has been set down in stone - literally - in the Ten Commandments, as a father might draw out his expectations clearly when they aren't first met. Through large and small actions, through providence and lacking, God teaches us to be humble, patient, honest, and contrite. Providing supervision, guidance, and discipline is fatherly.