The pope is called this because he spends his whole life on the catholic church so the apostles are the servants of god and the pope is the apostle's servant because he spreads on the catholic faith...
Servant of the Servants of God (in latin Servus Servorum Dei) was first used by Pope St. Gregory I (aka St. Gregory the Great), who reigned from 590 to 604 AD first used this as one of his titles. It...