Objection: I don't believe that God can use sinners who have not repented to infallibly proclaim His truth; some popes have been so bad that I just CAN'T acknowledge their authority!
Answer: Before I answer, I would like to point out that I purposely worded this one carefully to say "sinners who have not repented" because even the apostles were sinners, but they were sorry for their sins. Some Protestants might not be as careful in their wording and just say "sinners," but they mean people didn't live good Christian lives, as some of our popes have. Now, on to the actual answer. First, where does the bible say this? As far as I know, it doesn't. In fact, the book of Deuteronomy says that the Jews had to listen to the priests in their interpretation of the law (Deuteronomy 17:8-13), and it doesn't give any exceptions. Jesus was always criticizing the scribes and Pharisees; He even said that we must be more righteous than them to get into heaven (Matthew 5:20). He even condemned their "traditions of men" (Matthew 15:3-14)! However, He still told the people that they must follow their teachings because they SAT ON MOSES' SEAT (Matthew 23:2). Even though they were hypocrites and didn't practice what they preached, they still had to be obeyed because they were in positions of authority. Again, when the priests and Pharisees were plotting to kill Jesus, Caiaphas, the high priest, prophesied that Jesus would be killed for the whole nation (John 11:49-53). Even though Caiaphas rejected Jesus and was sinful, he was still able to prophesy because he was the high priest!
Objection: If the pope is infallible, then why did Paul publicly rebuke Peter, the "first pope" in Galatians 2:11-14?
Answer: The Catholic belief in papal infallibility says that the pope is infallible only in his teachings on faith or morals; NOT his personal practices. Here, Paul rebuked Peter for hypocrisy, which is a PERSONAL PRACTICE. Peter used to eat with the Gentiles, but he was pressured by the Jews to stop; this is what Paul was rebuking him for. Peter actually PREACHED that Jews and Gentiles were not separate and that they didn't have to follow the Law of Moses (Acts 11:1-18). Actually, this passage supports Peter's primacy. When Peter stopped eating with the Gentiles, other Jews joined him, even Barnabas (Galatians 2:13)! Peter was so influential that the Jewish Christians followed him instead of Paul; even Barnabas, who worked with Paul and defended the Gentiles at the Council of Jerusalem, followed Peter's example.
Objection: Paul said that he was not inferior to the super-apostles (2 Corinthians 11:5, 12:11). He had no belief in Peter's primacy.
Answer: I find it hard to believe that this is actually a common objection, but it is. Paul is being sarcastic here; he is referring to false teachers (2 Corinthians 11:4, 12-15).
Objection: At the Council of Jerusalem, Peter's testimony is heard, but James has the final word (Acts 15:13-21). If anyone had a primacy, it was James, not Peter.
Answer: Ok. After "much debate," Peter stood up and addressed the council (Acts 15:17), and after he spoke, the whole council "kept silence" and listened to the testimony of Paul and Barnabas (Acts 15:12). Right away, we can see that Peter had authority. He speaks after there had been much debate, and the whole council was quiet after he spoke. Now, why would Peter speak AFTER the debate? Because he was the first pope. He refers to his own God-given authority as "the one throgh whom the Gentiles would hear the message of the good news and become believers," not to Scripture or any other authority. After Peter speaks, everyone is silent as Paul and Barnabas describe the wonders that God had worked through them among the Gentiles. Next, James speaks, and he even refers to Peter's authority (Acts 15:14)! James isn't making a decision APART from Peter's; he is simply reaffirming Peter's decision. As bishop of Jerusalem, he naturally would have held a prominent place at the council.
Objection: Peter was never in Rome. He doesn't mention Rome in his epistles, and Paul doesn't mention Peter in his epistle to the Romans.
Answer: First, there is tons of historical evidence that Peter was in Rome. For quotes from the Church Fathers, check out Catholic Answers's Peter's Roman Residency. Second, Peter DOES mention Rome in his first epistle. In 1 Peter 5:13, he says that he is in "Babylon," which was the Christian "code word" for Rome. Third, Paul may have mentioned Peter in his epistle to the Romans. Paul says, "Thus I make it my ambition to proclaim the good news, not where Christ has already been named, so that I do not build on someone else's foundation...This is the reason that I have so often been hindered from coming to you" (Romans 15:20, 22). Paul may have been referring to Peter as the one who had already built the foundation in Rome. Fourth, there are a few plausible reasons why Paul wouldn't have mentioned Peter in his epistle: 1) Peter might not have been in Rome at the time. He may have been preaching elsewhere, but with Rome as his homebase. Also, Paul's letter could've been written when the Jews, including Peter, were expelled from Rome by Emperor Claudius. 2) Persecution was a very real threat during the first century, so paul could've been protecting Peter by not mentioning him.
Objection: In 1 Peter 5:1, Peter refers to himself just as an elder, not as pope or head of the Church. He was equal to all the other elders, no above them.
Answer: In 1 Peter 3:8, 5:3, Peter exhorts his readers to practice humility, and this is what he is doing in 1 Peter 5:1. If we take this to mean that he wasn't the head of the Church, then we should also take this to mean that he was just an elder and not an apostle. This, of course, is absurd. Let's give a modern example of this kind of speech. When the president of the United States addresses the nation, does he say, "I am the president, the highest authority in the land."? No! He addresses the nation as "My fellow Americans."
Objection: Peter was not the rock upon which Jesus built His Church. In Matthew 16:18 Peter is called "petros," which means a little rock, and the rock is called "petra," which means a large stone.
Answer: While this was true in ancient Greek poetry, petros and petra had become synonyms by the first century, with "lithos" being the word for a small rock. Since Peter was a man, Matthew had to use the word "petros" for him because that is a masculine noun, while "petra" is a feminine noun. Also, Jesus spoke Aramaic, and many scholars think the Gospel of Matthew was originally written in Aramaic. The word for both "Peter" and "rock" is "kepha," which is transliterated as "Cephas" (John 1:42).
Objection: All the apostles received the keys of the kingdom of heaven and the power to bind and loose in Matthew 18:18, so Peter having them doesn't make him special.
Answer: First of all, nobody but Peter received the keys. The apostles as a whole received only the power to bind and loose, not the keys. The apostles received the power to bind and loose as a whole, but Peter received it separately from the rest. The apostles as a whole could bind and loose, but only Peter could bind and loose by himself. Now, if all the apostles had the keys and the power to bind and loose just like Peter, then why did he get them before and separately from the other apostles?