As a general rule, if you want to understand a religion, a good place to look is to its leaders. Sometimes, this is hard. Who, for example, leads Islam? There is no single leader, nor body, of Islam. So, effectively, the leader of Islam is Muhammad, thus you go to his teachings. On the other hand, you have better organised religions, such as Mormonism. Mormons believe there is a modern prophet (currently Russel M. Nelson), and modern apostles, to whom their doctrines must be conformed. If you want to know about Mormonism, go to their teachings.
For Catholicism, the Big Big Cheese would be the Pope. According to modern Catholic belief, the Pope is the "visible head of the whole Church militant", sitting in the place of Peter, who allegedly received that position from Jesus Christ in Matthew 16:18. Catholicism also has a doctrine of Papal Infallibility, which is often misunderstood by non-Catholics. It does not mean the Pope is never wrong, and so I will not be arguing from that assumption in this article. As summed up by the Catechism of the Catholic Church, however:
""The Roman Pontiff, head of the college of bishops, enjoys this infallibility in virtue of his office, when, as supreme pastor and teacher of all the faithful - who confirms his brethren in the faith he proclaims by a definitive act a doctrine pertaining to faith or morals.... the infallibility promised to the Church is also present in the body of bishops when, together with Peter's successor, they exercise the supreme Magisterium," above all in an Ecumenical Council. When the Church through its supreme Magisterium proposes a doctrine "for belief as being divinely revealed," and as the teaching of Christ, the definitions "must be adhered to with the obedience of faith." This infallibility extends as far as the deposit of divine Revelation itself." (CCC 891).
From this, we see that the Catholic Church does not teach that the Pope is infallible. It does, however, teach that he can be. In order to be infallible, he must be speaking "ex cathedra" (i.e. with the fullness of his alleged authority, as tied to his office as Pope), defining a doctrine that concerns faith and morals for the whole Catholic Church. For reasons I consider to be obvious, this doesn't happen very often. In fact, it is so rare that it is often disputed within the Catholic Church as to exactly when it happens.
But one thing is for sure: We should expect the "visible head" of a religion to at least know, and be consistent with, the teachings of that religion, especially if you believe there is the possibility he could ever be infallible. It makes no sense for the Pope to be able to define doctrines for the entire Church in one capacity, but for the rest of his life be radically out of step with the allegedly infallible teachings of that Church.
Now, it's one thing for the Pope to voice his opinion on gun control and suggest his view is the Christian one. It's another thing entirely, when the Catholic Church has historically taught that there is no salvation outside their Church, for him to crouch down to a little boy and tell him his atheist father is in Heaven and can be prayed to. Yet, this is what he did, and he is quite in step with the Catechism of the Catholic Church, as promulgated by his predecessor.
Regardless of the truth value of their religion, most religious leaders are fairly capable of consistency. This is not always the case, of course, and leaders of false religions do tend to conflict with their predecessors. Nevertheless, it seems absurd to me to think we should expect less of the Pope than from other religious leaders. If I ask a religious leader a question about their religion, I fully expect them to be able to answer it, especially if it is so critical as "how do I get saved?"
But this is not the case for Pope Francis, nor for his most recent predecessors. Indeed, whereas the Council of Trent "infallibly" anathematises all "Protestants", the Catholic Church gradually came to instead consider us "separated brethren", or more recently "other Christians". What we see, then, is that the alleged leader of the Catholic Church is less committed to his religion than even the most insane of cult leaders are to theirs.
So how dare he claim a title the Bible ascribes to Christ?
Biblically speaking, Christ, not the Pope, not even the legitimate Apostle Peter, is the head of the Church (Ephesians 5:23; Colossians 1:15-18). You will search the scriptures in vain for references to another head, visible or otherwise. And so it is clear that the Pope claiming this title is just one more example of a Catholic claiming the glory that God says he will share with no other (Isaiah 42:8; 48:11). The Pope leads the Catholic Church, though poorly even by their own reckoning, but he does not lead Christ's Church. This should cause Catholics to ask, if he is not leading them by Christ's authority, where is he leading them to? If Christ is the one and only way to the Father, will he who leads apart from Christ lead to the Father? Beware the false teacher. Let his condemnation be his own. But to you who love Jesus, I have only one charge: Flee the Catholic Church.