I think your example is perfect Brother and I understand what you mean by it.
The reason why I confront on the Muhammad point is that it seems like the only intellectual reason to abandon the Muslim faith. Sometime ago in my own life, I was uncertain as to why I should be Catholic and not Muslim. The common answer I got was that if you were born in to it, that is what you will be and its highly unlikely that you will have intellectual reason to move out of it.
I have heard some say that any other non-Catholics could identify with the positive things of our faith but I am not so sure about it anymore. There are so many non-Catholics, especially Atheists who will ridicule positions of our faith that are morals, faith, and even canon law. I also find that when I explain to them on how to make sense of these positions of our Church, they will still ask why I would believe in it and the theology behind it. This strikes me as a valid question and certainly one that needs an answer.
So what/how I made sense of all of this is by asking how do I know which religion is true. It seemed to me that everything that mattered in each religion were its claims on the Transcendent. The Transcendent would be outside of our direct experience to verify. So one would have to ground the knowledge in someone who can reveal it to us.
The issue then is that this person one chooses to rely on for knowledge regarding the Transcendent has to show that they are reliable. So every religion on earth can be analyzed to see if the founder of the religion is reliable. In the case of Zeus, Thor etc, we have a negative answer since no one who came up with these myths can be credited to have any authority. Also, Zeus and Thor tend to be Gods of the gaps. They tend to be described as the lightning or some other physical phenomena itself. So scientific knowledge can also disprove the non-existence.
With figures like Buddha or Muhammad, neither performed any acts for us to make us believe them. Buddha they say could speak to animals. But this does not say that he has authority of the Transcendent. Muhammad they say became literate all of a sudden and compiled/recited a text such as the Bible. This too is not that impressive since any person could educate themselves to the point of reciting a narrative/instruction etc.
Christ on the other hand, died and rose from the dead. Something we cannot yet reproduce and something we know ancient societies were incapable of performing. So Christ seems worthy of our assent, at least from the perspective of learning knowledge to resurrect ourselves. In this way, then one can justify assent to the Apostles since they were his students and the students/successors of the Apostles since they were the students of the first Apostles and so forth.
At this point, a Muslim might say Muhammad claims that Jesus never died. But since we have already dismissed the idea of assenting Muhammad’s claims as divine, his claim on Christ must be purely historical. However, Muhammad lived almost 600 years after Christ. So it seems unreasonable to believe a claim made 600 years later over those who lived proximately to the event.
A word about the Jewish faith, one might ask why believe in Moses. I would say it reasonable to believe in Moses for the Jewish people since their forefathers had a very testing experience with him. They doubted if Moses was indeed from God. They tried disobeying his commands. But they got punished. This happened more than once. So the Jewish people, in a sense, verified to themselves that God was indeed speaking through Moses. The only issue here is that it is perhaps unreasonable for someone outside the Jewish lineage to give assent to it because they do not have the same level of trust in Jewish forefathers.
I feel that this is an intellectual way to arrive at Catholicism (or Judaism as a precursor to Catholicism) and also discard all the other religions as false.
I also feel that the method of simply discussing and explaining our own position is not enough to pursue someone to abandon ones faith, especially since it is cultural. We would only be able to appeal to the preferences of the person in this way. So unless a person has already grown up with a preference for Catholic positions that do not exist in their own, they will be less likely to embrace the Catholic position.
I also feel that while sometimes they might accidentally agree and even state Catholic positions as their own. They will tend to backtrack and oppose that position for what it is (i.e. something they liked out of preference) and uphold their own as what they truly believe. Or there are those who would discard some of their own and try to have a mixed Catholic-Islamic faith. I think this is dangerous because underneath, they hold the idea that no religion could be identified as the true religion through reason. So they must go with preference.
This idea also seems to pour over to the moral plane. There are even Catholics, who consider that the moral plane which deals with the Transcendent, has to rely on preference/consensus. They argue that what is a Church or a Religion to tell them what morality might be. I find that their position is indeed true and they too ask a valid question. If a Church or Religion cannot give actual reasonable grounds to accept them as the reliable authority regarding the Transcendent, why should anyone give assent to them?
So I find, in my personal experience, that not confronting the actual problem of all these other religions having no authority to be the sole issue. Because right now, I feel the Atheist or non-Catholic are asking very valid questions of the authority of the Church or of any other religion to dictate truths regarding the Transcendent through them. If we try to stand together with other religions, we only make ourselves look unreasonable as well?