Let’s take a look. The atheist’s argument is that there isn’t enough space to fit in so many animals, so the story is not true. Here, his faith is not so much in the story as in the physical law that the volume of animals that you put into an enclosure cannot exceed the volume of that enclosure. To him, this physical law is inviolable. So either there weren’t so many species on board, or the ark was much bigger. If there were far fewer species, it cannot explain the diversity that we see today – a contradiction with his faith in the world as seen. An ark of the size that would hold all the species, on the other hand, might be structurally/practically impossible to build – thus contradicting his faith in structural mechanics or common sense. That leaves him with the conclusion that the story is false.
Theist versus atheist
From a believer’s perspective, the story and God’s glory are established beyond doubt. If it is physically impossible to carry all species of plants and animals on a wooden ark, then it just means that the glory of God and his chosen ones are not bound by physical laws. The “evidence” that was worked out to shake his faith in God has now turned into a miracle that will only reinforce his faith.
Take another story from the Bible, where Jesus feeds 5000 with 5 loaves of bread. It is pointless to work out the maths that each will get only one-thousandth of a loaf of bread which won’t be enough, because that’s exactly the reason why it is called a miracle.
On the surface, it might seem that the atheist’s claims and thought process is rational while the believer’s isn’t. But it doesn’t necessarily have to be so. Both the believer and atheist can have perfectly rational and consistent set of thoughts that lead to mutually incompatible universes based on the fundamental assumptions being made by either one. Logic only demands that this set of assumptions be consistent with itself (i.e., assumptions within a set do not contradict each other). It doesn’t require, nor can it validate, the truth of these assumptions.
This is similar to how we can construct alternate, self-consistent, geometries that produce drastically different results, depending on the axioms that we accept as true. It won’t be possible to refute any of these geometries or find the best one among them solely by reason, because they are all true to their own faith.
Now, unlike the case of Noah’s ark, there could be elements in religion that are self-contradictory from a rational point of view. A most common example is the question of whether an omnipotent God can create a rock that he cannot lift. A rationalist would take this contradiction to rule out omnipotence, but for a believer it just means that God is beyond rationality. After all, rationality is a construct of finite human intelligence and there is no reason for the infinite God to be bound by it.
Believer and rationalist are lines in two different planes
At this point, it is clear that any debate between this believer and a rationalist on anything that involves God is meaningless, because their arguments are like lines (of thought) that are neither parallel, nor intersect, for they are on two different planes. This is why I consider most of the debates and discussions in which an atheist or a theist are trying to convince and convert the other or prove them wrong as futile, because there is no common set of rules by which their arguments can be judged.
If at all they do want to engage in such a debate. it should probably start by identifying a set of basic truths that they can both agree to, and then use them to contradict the other’s claims. This, again, is possible only if they both agree that the truth being discussed is subject to reason and logic.