To what extent can a religious believer actually argue their faith, reasonably? Not very far, it seems to me.
There are two quantities to consider here, by which all human beliefs can relate back to: Faith and Evidence.
Let's look at the first. Faith, by its very definition, is 'belief without evidence'. It is a gut feeling, and it cannot be proven wrong. Why? Because, for something to be 'proven wrong' evidence has to come into play, and Faith stays strong regardless of counter-evidence to its claims. When considering God, the only argument one can ever draw is that 'God can't be dis-proven'. Whether this is a strong argument or not for a specific religion's creator is irrelevant - people still use the argument, failing to accept/realise that it can also be applied to Zeus, or Santa...
The other side of the attempt to justify religious claims is, well, to say that there is evidence for them. I of course disagree with this post-hoc, presumptuous mindset, but I can see why people like Pope Pius XII have, over the years, jumped at the chance to declare that science has proven what they knew all along. It's a simple desperate grasp at reconciliation with reality.
Why do I mention Pius? Well, in response to The Big Bang Theory in 1951 he made this claim:
"It would seem that present-day science, with one sweep back across the centuries, has succeeded in bearing witness to the august instant of the primordial Fiat Lux [Let there be Light], when along with matter, there burst forth from nothing a sea of light and radiation, and the elements split and churned and formed into millions of galaxies. Thus, with that concreteness which is characteristic of physical proofs, [science] has confirmed the contingency of the universe and also the well-founded deduction as to the epoch when the world came forth from the hands of the Creator. Hence Creation took place. We say: "Therefore, there is a Creator. Therefore God exists!"