The Short Answer
The best answer is simply that the Bible says nothing positive about popes and cardinals. It doesn’t take many words to point out an absence of evidence. I will require many words, however, because it is not so simple to refute rationalizations for violating what the scriptures do say.
Titles Are Not "Wrong"
In a hierarchy, it is desirable to give titles to different levels. For example, in a corporation, you might have a president, several vice presidents, managers, and supervisors. Even Moses, upon the advice of his father-in-law, appointed levels of supervision. The New Testament has words such as deacon, elder, shepherd, and bishop, and they are used descriptively rather than as titles. Man focuses on titles, but God focuses on the work.
Industry, especially the software industry, is returning to the model of allowing people to self-organize, at least at the bottom levels, because they know what needs to be done and how best to accomplish it. This trend is called “Agile” and helps produce more value sooner, especially in changing environments.
Similarly, the New Testament is intentionally ambiguous so that creating offices such as Pastor, Bishop, and Cardinal is left to individual churches. Not every model, such as independent churches versus worldwide denominations, fits every political and cultural environment. So the fact that the scriptures do not spell out a title is not enough reason to reject it.
The Unbiblical Title and Role of Pope
The title of Pope, however, is strictly anti-biblical — and worse. Jesus said, Call no man your father on earth, for you have one Father, who is in heaven. (Matthew 23:9) One rule of Bible interpretation is, if the plain sense makes good sense, any other sense is probably nonsense. It is not only anti-biblical to call a priest Father, but also to call a man Pope.
Further explanation ought to be unnecessary, but I anticipate heated objections, so I’ll elaborate.
When we consider the title, Pope, we must first recognize that it comes from Greek papas, father. This is echoed in another title of the pope, Holy Father. In Mark 10:18, Jesus said, Why do you call Me good? No one is good except God alone.
There are many similar statements with the term holy, such as 1 Samuel 2:2, There is no one holy like the LORD, Indeed, there is no one besides You, Nor is there any rock like our God. Goodness and holiness can be ascribed to God alone. Peter would have been appalled at being called Father or Holy Father.
Do you see a trend, yet?
In John (see 14:16, 14:26, 15:26, and 16:7), Jesus gave a descriptive title to God the Holy Spirit: Paraclete, which has the meanings of comforter and advocate. He described the Paraclete (Holy Spirit) as coming in His place, to be His vicarious Presence. That meets the definition of Vicar of Christ (substitute for Christ).
Catholicism puts these usurped titles into action by placing its “Fathers” between believers and God, discouraging non-clergy from fully enjoying the personal relationship that God desires to have with his children. All three members of the Triune God fulfill the relationship without human interference:
The Son -- He [God the Son] is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them. Hebrews 7:25
The Spirit -- In the same way the Spirit also helps our weakness; for we do not know how to pray as we should, but the Spirit Himself intercedes for us with unutterable groanings; and He who searches the hearts knows what the mind of the Spirit is, because He intercedes for the saints according to [the will of] God. Romans 8:26–27
The Father -- Let us then approach God's [the Father’s] throne of grace with confidence, so that we may receive mercy and find grace to help us in our time of need. Hebrews 4:16
The system instead inserts itself between people and God, encouraging people to bring their prayers to its priests, to believers in heaven, and to angels — as though they had the omnipresence and omniscience that allows God to receive all prayers.
No First Pope
Before closing, one more issue, and a tangent, need addressing. You will observe circular reasoning that Peter was the first pope, so the papal office is legitimate, so the first pope was Peter.
First, nobody called Peter a pope until hundreds of years later. The proof text, Matthew 16:15–19, used by Catholic teachers, simply does not call him pope, and it does not give him the extent of authority they claim.
Christ Is the Rock
The rock on which Christ said He would build His church is Peter’s confession. You can see Peter as being the rock only if you are biased to see it that way. In the Greek, Peter is masculine gender petros whereas rock is feminine gender petra. A petros is a stone whereas a petra is a monolith. If Jesus had meant Peter was the rock, He would have used the same word, saying You are Peter (petros) and on this rock (petros) I will build my church, not on this rock (petra).
To the contrary, the Bible gives the title of Rock to God the Son, as in 1 Corinthians 10:4, that rock was Christ, and as in 1 Samuel 2:2 (above). Even Peter himself identified Christ as the Rock toward the end of 1 Peter 2:4–8, and anyone who grasps biblical metaphor can understand that “rock,” Christ, extends to the recognition of whom Christ is — the core of the gospel. Again, Catholic teaching misapplies a title that belongs to God alone to a human.
Keys to the Kingdom Fulfilled in Acts
Catholic teaching says that the keys to the kingdom and the power to bind and loose refer to total authority over the church. That is inconsistent with the rest of the New Testament. Act 1:8, the theme verse of that book, declares, you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth. Acts describes the expansion of “God’s people” from the disciples, to Jews in Jerusalem, to Judeans, to Samarians, to the gentiles. Peter was present for each of those expansions, and the gifts of the Holy Spirit were opened up to those concentric groups through him.
However, Peter did not remain at the head of the church’s earthly hierarchy, as it had another president long before Peter left the scene (Acts chapters 15 and 21).
Catholic Bishops are Unqualified
Second, the Catholic explanation avoids the apostle’s description of a bishop’s qualifications. The Catholic will say that the bishop is married to the church, but Titus 1:4–9 specifically speaks of not only a wife, but also children. Indeed, Paul pointed out how Peter, Jesus’ brothers James and Jude, and other apostles each had wives, and had a right to have wives, in 1 Corinthians 9:5. Paul clearly teaches that God makes some people for marriage and others for single lives. Imposing celibacy on all clergy is strictly anti-biblical.
On a metaphorical level, it violates common sense for the church (the body of all believers) to take multiple human husbands when it is already the future Bride of Christ. (Ephesians 5:25-27, Revelation 19:7-9) Likewise, it makes no sense for the married apostles to have both earthly and corporate wives. Thus, the Catholic priesthood usurps yet another title and role of God, that of divine Husband.
The Sin of Papal Veneration
Catholicism gives to its chief the titles and roles of Holy, Holy Father, Pope (papas), Paraclete, Vicar of Christ, intercessor, husband of the church. It delegates those roles and titles, in reduced form, to its local representatives. These titles all belong to God. Catholic priests may have been taught that God delegates these to them, but the claims contradict the Bible. I am the LORD, that is My name; I will not give My glory to another, Nor My praise to graven images. Isaiah 42:8 Usurping the titles and roles of God is a severe form of blasphemy.
Over a millennium of rationalizing does not make the rationalizing any less sophistic. It is worth considering whether allegiance to an organization that creates new standards (traditions that morph with the culture) in order to justify contradicting the unchanging original standard (the scriptures) is the right choice.