Don't all the Apostles receive the keys to the kingdom, making them equal with Peter?
Let's examine this briefly by first turning to the two relevant passages where Peter receives the keys of the kingdom in conjunction with binding and loosing, and the second one where all the Apostles are given the authority to bind and loose.
Matthew 16:19, Jesus speaking to Peter: I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.
Matthew 18:18, Jesus speaking to the Twelve: Truly, I say to you, whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.
The relevant point here is that Matthew 18 nowhere uses the Greek term kleidas (keys). That term is only found in Matthew 16, and it is applied in the Greek singularly to Peter alone. "Doso soi tas kleidas." "I will give to YOU (Greek singular) the keys." In Matthew 18, the Apostles are collectively given the authority to bind and loose, and the "You" here is in the plural for that very reason. Not singular. In union with Peter, who alone is said to possess the keys, they also can exercise the authority to bind and loose. Peter, apart from them, can do this on his own, as he alone is given the keys singularly, and he alone is given the prerogative to bind and loose. The Greek is very clear on this.
The Protestant book Commentary on the Whole Bible, compiled by Anglicans and Presbyterians, admits: "Keys are figurative for sustaining the government on one's shoulders." Eerdmans Bible Dictionary, also Protestant, regarding Matthew 16:19, admits: "In accordance with Matthew's understanding of the kingdom of heaven (i.e., of God) as anywhere God reigns, the keys here represent authority in the Church."
The keys do not belong to everyone. Jesus gave them to Peter singularly, and Peter had successors. That list continues unbroken to this day.
St. Augustine, 4th century, traces the Bishop of Rome in his day directly back to St. Peter: "For if the lineal succession of bishops is to be taken into account, with how much more certainty and benefit to the Church do we reckon back till we reach Peter himself, to whom, as bearing in a figure the whole Church, the Lord said: "Upon this rock will I build my Church, and the gates of hell shall not prevail against it!" The successor of Peter was Linus, and his successors in unbroken continuity were these: -- Clement, Anacletus, Evaristus, Alexander, Sixtus, Telesphorus, Iginus, Anicetus, Pius, Soter, Eleutherius, Victor, Zephirinus, Calixtus, Urbanus, Pontianus, Antherus, Fabianus, Cornelius, Lucius, Stephanus, Xystus, Dionysius, Felix, Eutychianus, Gaius, Marcellinus, Marcellus, Eusebius, Miltiades, Sylvester, Marcus, Julius, Liberius, Damasus, and Siricius, whose successor is the present Bishop Anastasius. In this order of succession no Donatist bishop is found."
In 251AD, St. Cyprian of Carthage wrote, "On him he builds the Church, and commands him to feed the sheep, and although he assigns a like power to all the apostles, yet he founded a single chair, and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were what Peter was, but a primacy is given to Peter, by which it is made clear that there is one Church and one chair… If someone does not hold fast to this unity of Peter, can he think that he holds the faith? If he deserts the chair of Peter upon whom the Church was built, can he be confident that he is in the Church?"
In 431AD, the Council of Ephesus singled St. Peter out alone as possessing the keys: "The holy and most blessed Peter, prince and head of the apostles, pillar of the faith, and foundation of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ… who down even to today and forever both lives and judges in his successors. The holy and most blessed Pope Celestine, according to due order, is his successor and holds his place."