"On that day I will summon my servant Eliakim, son of Hilkiah; I will clothe him with your robe, and gird him with your sash, and give over to him your authority. He shall be a father to the inhabitants of Jerusalem, and to the house of Judah. I will place the key of the House of David on his shoulder; when he opens, no one shall shut, when he shuts, no one shall open."
- Isa 22:20-22
"And so I say to you, you are Peter, and upon this rock I will build my church, and the gates of the netherworld shall not prevail against it. I will give you the keys to the kingdom of heaven. Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven."
Many biblical scholars agree, whether Protestant or Catholic, that Mt 16:18-19 is an allusion to Isa 22:20-22.
Many Protestant scholars have had to agree with the Catholic interpretation of Mt 16:18-19. It is the only logical explanation. A prestigious Protestant scholar once said that the only reason many Protestants don't interpret Mt 16:18-19 to be Jesus building His Church on Peter is because they are biased against Catholics. It has nothing to do with proper biblical interpretation.
The Catholic interpretation (and the interpretation of the Church Fathers) is that it is not just Peter's faith Jesus is building on but Peter himself. Jesus is saying He is building His Church on Peter the rock. Mt 16:18-19 points out Peter's exclusive position in the Church, having received this authority from Christ himself. And it is an allusion to the old testament scripture, in Isa 22:20-22, something Mathew's gospel does quite frequently. Scholars agree 'Keys of the kingdom' means teaching authority.
Also, Eph 2:20 further states the Church is built upon the Apostles with Christ as the chief cornerstone. So, it is not Christ or Peter. Rather, the Church is built on both Christ and Peter, including all the Apostles.
"The blessed apostles [Peter and Paul], having founded and built up the church [of Rome] . . . handed over the office of the episcopate to Linus" (Irenaeus, Against Heresies 3:3:3 [A.D. 189]).
"[T]he Lord said to Peter, ‘On this rock I will build my Church, I have given you the keys of the kingdom of heaven [and] whatever you shall have bound or loosed on earth will be bound or loosed in heaven’ [Matt. 16:18–19]. . . . Upon you, he says, I will build my Church; and I will give to you the keys, not to the Church" (Tertullian, Modesty 21:9–10 [A.D. 220]).