Thanks to everyone who has responded thus far.
Here’s an example of making the case for Catholicism by Catholic Answers’ own Jimmy Akin:
Both Protestants and Catholics agree that Christ founded some Church and that this Church will remain forever (Matt. 16:18). The question is whether this Church is a visible communion that can be identified or whether is it a purely spiritual communion made up of all the saved. If it is a visible communion, the Catholic Church is the only plausible candidate, since only this Church extends back far enough… . We can thus give a limited argument for the [idea that to be a member of Christ’s Church it is necessary to be a member of the Catholic Church] by showing the Church Christ founded is a visible communion.
This is proven in Matthew 16:17-19, the passage in which Christ promised the gates of hell would never prevail against his Church (meaning that it would always exist). Several factors in the text show he was talking about a visible communion.
First, Jesus made Peter head of this Church (Matt. 16:18), yet Jesus was certainly not making Peter the head of an invisible Church. It is Christ’s own prerogative to be head of the invisible communion of Christians stretching from heaven to earth (Eph. 5:23). Therefore, he must have made Peter the head of a visible, earthly church. (We will not argue here that Jesus made Peter the head; even if one disagrees, the remaining arguments prove our case.)
Second, Jesus gave Peter the keys to the kingdom of heaven (Matt. 16:19), which are for use in Church government (compare Isa. 22:22 – the only Old Testament parallel to this verse). But one cannot govern an invisible communion of believers, only a visible one.
Third, Jesus gave Peter the power of binding and loosing (Matt. 16:19), which Matthew 18:17-18 indicates is used in Church discipline. But one cannot exercise Church discipline over an invisible body. Indeed, Matt. 18:17-18 refers it to public excommunication, in which an individual is treated by the church as “a gentile or a tax collector” (that is, as an unbeliever).
Fourth, Jesus explicitly stated that Peter would exercise the power of binding and loosing on earth. This shows his authority is an earthly one, over an earthly Church.
Fifth, Jesus promised the gates of hell would not prevail against his Church (Matt. 16:18), meaning that it would never perish. But it would be ridiculous to promise that an invisible Church would not pass out of existence since some of the Church’s members are in heaven and Christ’s heavenly Church cannot pass away by its very nature. Only a visible, earthly communion needs a promise that it will never perish.
There are thus abundant reasons to conclude that the Church Jesus was discussing in Matthew 16:17-19 was a visible communion of believers, and, since only the Catholic Church goes back that far, only it can be the one Christ founded.
From:
The Necessity of Being Catholic
by James Akin
chnetwork.org/journals/nesschurch/ness_7.htm