I can understand why we call the pope “Father,” as he is an ordained bishop. But why do Catholics call the pope “Holy”? Why would a sinful person be called “Holy”?
In common parlance, people tend to think the word holy means “super saintly.” Actually, holy means to be “dedicated or consecrated to God or a religious purpose; sacred” (source). The pope is honored with the title “Holy Father” because, of all the fathers on earth (both natural and supernatural), the pope is the one most especially set apart for the service of God and man as Vicar of Christ on earth.