As we all know, though, more than half the Christian world disagrees. I say "more than half" because, even though about half of all Christians were baptized in the Catholic Church, many educated Catholics reject what I've just said the Church has shown me. The two most common objections to Catholicism one hears from educated Christians, including some who are nominally Catholic, are: (1) Distinctively Catholic doctrines are not rationally necessitated by the early sources, and so shouldn't be thought to belong to divine revelation as distinct from human tradition, and (2) The course of Catholic doctrinal development yields internal inconsistency at the highest level, so that the Church's claim to infallibility--even under limited conditions--is not credible. It might be useful to others for me to state here, in baldest outline, what I offer as answers to such objections. Such a way of organizing the arguments, if sound and taken to heart, would save a lot of people a lot of wheel-spinning.
(1) misconceives the nature of divine revelation and the assent of faith thereto. Divine revelation does not consist primarily in a set of propositions to be inferred from writings and other evidence from the past. Such things, to be sure, are indispensable for preserving the Church's collective memory of what's been handed on by the Spirit through Sacred Tradition. Yet at bottom, what's handed on is the reality of the decisive encounter between God and man in Christ Jesus. Forms of words, archeological evidence, comparative religion, and so on merely help express that. Now if Christianity is true, then by God's design, the ongoing encounter between God and man takes place through something called "the Church" even though, as is the case with many who hear the call to faith in Christ, it needn't start in the Church. Yet without being in any way limited to the authority of the Church, said encounter always and necessarily depends on a visible, clearly identifiable ecclesial authority which exercises God's own authority as revealer and sanctifier. For without such an authority, the content and power of divine revelation would end up appearing only as a matter of opinion. That, for us, would be no revelation at all, and assent to it, such as it is, would be no faith at all. Despite how different they are in many respects, Aquinas and Newman made essentially that argument. Following them, it's one that I've long made myself.
What about (2)? As an argument, it begs the question either at the outset or in the end. In some formulations it premises, as the only reasonable ones to adopt, interpretations of Catholic doctrine that yield contradictions. But if the Magisterium's claims for itself are true, said premise is false. There must be other reasonable interpretations of Catholic doctrine that are collectively self-consistent, and those turn out to be just the ones the Magisterium itself, the author of the doctrines in dispute, has come to adopt. Given as much, the objector needs to show that interpretations yielding contradictions are ones that the Magisterium itself once adopted, and did so in such a way that its own criteria for infallibility were thereby satisfied. But those who press (2) usually don't try to show that. When they do, they end up begging the question all over again—by assuming a way of applying the criteria for infallibility that the Magisterium itself would reject.
Now it should go without saying, but often needs to be said, that successfully rebutting (1) and (2) does not prove Catholicism to be true. Indeed, given the Catholic understanding of how reason and faith are interrelated, nothing could "prove" Catholicism to be true. Faith is a divine gift that can only be accepted freely. If there were compelling arguments for Catholicism, then those who recognize as much would be compelled to believe, which is not faith. The role of reason in coming to faith is to show that faith is fully compatible with reason, not that reasoning compels it. That, of course, does not rule out the possibility that there are compelling arguments against Catholicism. But it is precisely the task of apologetics to show that there are no such arguments. In this post I've sketched two examples of how to carry out that task. I've elaborated those examples elsewhere, especially on this blog.