Bible
Is the Pope really the head of the Church?
That depends on which Christian tradition you ask, and it comes down to how one key Bible passage gets read.
Catholic teaching holds that Jesus made Peter the first Pope, based on his words: "you are Peter, and on this rock I will build my church." Catholics believe that authority passed down through an unbroken line of Peter's successors, the bishops of Rome, making the Pope Christ's earthly representative with real authority over the whole Church.
Most Protestants read the same passage differently—some understand "this rock" as Peter's faith or his confession that Jesus is the Messiah, not an office meant to be handed down as an ongoing institution. Protestants and Orthodox Christians alike generally hold that Christ alone, not any human leader, is the Church's true head.
Orthodox Christians historically honored the Bishop of Rome with special respect among equals—but never accepted authority over the entire Church, one of the causes of the historic 1054 split between Rome and Constantinople.
Bible quotations in these answers are generally taken from the Christian Standard Bible®, Copyright © 2017 by Holman Bible Publishers. Used by permission. Christian Standard Bible® and CSB® are federally registered trademarks of Holman Bible Publishers. Some biblical wording may be paraphrased or follow other translations.