To one who has faith, no explanation is necessary.

Theorem:
Any brand of Christianity, Judaism and Islam that claims to be the only true religion, is a false religion.

Proof:
There are thousands of theistic religion in the world; past and present. So if only one of them is true, the a-priory probability of it being true is less than one in a thousand. Even less; because it's possible that all theistic religions are false (which is the case if God doesn't exist; but that hypothesis is not needed for my proof). Therefore, any theistic religion that claims to be the only true religion is a-priori almost certainly false.

Now, in order for one theistic religion to be true while all others are false, it should provide evidence why it is so.
Theistic religions all rely on prophets. Meaning: People who claim to communicate with and from the Gods the theistic religions worship.
One possibility for a religion to make a case why its prophets speak for God and the others don't: Its prophets are exclusive and only used for that religion. This is not true for either of the Abrahamic religions. They all share prophets.
Next possibility for a theistic religion to be true: The messages received from their Gods are free of contradictions. In Abrahamic religions, God is supposed to be perfect.
But in all three Abrahamic religions, the "holy books" (Tora, Bible and Quran) are full of contradictions.

Conclusion: All three Abrahamic religions fail to make a case why they are supposedly the only true religion.
So if they insist on only one true religion existing while all others are false, then they themselves fail the test.
Q.E.D.