Seeing the coherence or “fit” of a system of ideas with certain other ideas that you already hold is not the same as seeing the truth of that system. Seeing that ideas you already accept are strongly supported by some system of ideas is not the same as seeing the truth of that system. Seeing the internal coherence of a system of ideas is not the same as seeing the truth of that system of ideas. Truth is a matter of thinking or speaking about things as they are. Truth is a relation between an idea about a thing and that thing itself. Seeing the truth of an idea is seeing that the idea is adequate to the thing itself of which it is the idea.
I think many people convert to Roman Catholicism because they are confronted with a system of ideas with which their own prior ideas fit nicely. Perhaps they even find in this system a better “support” for their own ideas than they previously thought themselves to have. Or else they are confronted with a system of ideas which is prima facie coherent and which fit together nicely with each other. But that is not the same as seeing that the ideas themselves are true. Roman Catholicism may be a coherent system of ideas on its own. That does not mean that it is true. The truth of these ideas has to determined by consulting the things themselves to which they refer.
A coherent system of ideas has a certain attractive quality about it. As soon as one considers in one’s mind a system of ideas that mutually support each other and fit together nicely, one is inclined to accept their truth. But this is a trick of psychology. A false collection of ideas can also seem true and one might be inclined to believe it. Contradictory sets of ideas can both “seem true” considered on their own as sets because the ideas all cohere with one another and yet both sets of ideas cannot be true in fact.
The Bible itself admits this point: “The one who first states a case seems right, until the other comes and cross-examines” (Prov. 18:17). When people state their case (e.g., in a courtroom or in the retelling of a conflict), we are considering what they say as ideas in the abstract. And so long as we are simply considering the ideas in the abstract, their coherence with one another is enough to make us inclined to believe them, assuming they don’t openly contradict what we take ourselves to know already. But we confuse this inclination to believe with the truth of the ideas themselves. Then another, incompatible set of ideas can be proposed and the coherence of that collection of ideas makes us inclined to believe that it is true. They cannot both be true, and yet we can be inclined to believe both. Thus, that inclination to believe is not a sense of the truth of the ideas but rather of their coherence with one another.
People who are “wading in the Tiber,” so to speak, ought to distinguish in their minds the attractive force of a coherent set of ideas and the actual truth of the ideas themselves. Before long, you will find that the actual reason for accepting the truth of those Roman Catholic ideas is not because they can be shown to be true to the things themselves but rather fallacious and unconvincing arguments, arguments one would not accept from the proponents of other religions, e.g. the Church is reliable because of miracles, or because of holy people, or because it is an ancient religious system that has survived to the present day, or whatever.