Ah, Matthew 16:18-19, one of the most misunderstood verses in the NT because people don't know the Greek.

Simon is called Petros in the Greek here. However, when Christ says "on this rock I will build my church", He uses petra, not petros; the feminine form instead of the masculine form for Peter's name. This change in grammatical gender reflects a difference in connotation. Petros referred to a small stone, whereas petra refers to a larger rock formation like a cliff or a boulder. If Christ meant to say that Peter was the rock upon which the church was built, then He would have continued to use petros instead of switching to petra. If Christ Himself switches to a different word with a different connotation, then it is self evident that He is speaking of two different things.

Further confirmation is found in 1 Corinthians 10:4, where Paul writes, "They drank of that spiritual Rock that followed them: and that Rock was Christ." Here Paul explicitly states that the rock is Christ, and he uses petra, not petros.

Putting these passages together, Christ designates Simon as Petros, the little rock, that points to Petra, the Rock, Christ Himself, who is the true foundation of the church.

Peter himself states that Christ is the Rock in Acts 4:10-11, where during his sermon he identifies Christ as the cornerstone that was rejected, a fulfillment of Psalm 118:22. This would have been the perfect opportunity for Peter to declare himself to be the cornerstone of the church, but he does not, pointing to Christ instead. Paul echoes the exact same sentiment in 1 Cor. 3:11.

If Christ unequivocally designated Peter as the head of His church, why then did the disciples repeatedly argue among themselves who was greatest? The fact that they held multiple debates on who was actually in charge demonstrates that Christ did not explicitly put one of them in charge of the whole church.

At no point in scripture is Peter ever cited as the head or pastor of any church. He was of course an influential evangelist and leader in the early church, but no one in scripture treats him the way catholics treat their pope. Even when the elders and apostles meet to discuss matters of doctrine, as in Acts 15, Peter is never depicted as issuing declarations that everyone else bows down to. Acts 15 records Peter, James, and others providing input as equals, with the apostles agreeing together to write and send the letter mentioned in verses 22-29.

In fact, Peter is corrected and rebuked by other apostles such as Paul, as recorded in Galatians 2:11-14. Peter evidently revered Paul as a fellow apostle and fellow author of scripture from his comments on Paul in 2 Peter 3:15-16. So much for papal infallibility or supremacy.

Furthermore, there is no historical evidence that Peter was the head of any church, much less the one in Rome. There isn't even any historical evidence that Peter ever visited Rome save for his alleged crucifixion there. Peter being a bishop in Rome is complete conjecture created by the RCC to grant themselves a false sense of legitimacy via apostolic succession. Which is itself another fabrication with no biblical support whatsoever. One of the qualifications for apostleship is witnessing the resurrected Christ in person (Acts 1:21-22, 1 Cor. 9:1). Paul was the last person to have done so; no one after him could ever even qualify for apostleship.

Lastly, even if Peter started and led a church in Rome, it is self evident that the RCC has completely invalidated itself from being his successor. Nearly every doctrine that is distinctive of the RCC is either complete fanfiction that has no biblical support, or outright contradicts the clear teaching of scripture. Such doctrines include but are not limited to transubstantion, purgatory, salvation by works, confession to priests, banning priests from marriage, making priests separate from the laity in the first place, the eternal virginity of Mary, the sinlessness of Mary, prayer to deceased saints, replacement theology, etc. The mere fact that the RCC both viciously persecuted Jews for over a millennium and also prohibited the laity from reading the scriptures for themselves for over a millennium puts them at odds with the apostles and Christ Himself.