Cherry picking facts is detrimental in a lot of respects, and here is an example of how it can be detrimental to two different persons doing natural theology.
Person 1 defends the following thesis: The probability of atheism given the evidence is not only higher than the probability of theism given the evidence, but it is more likely than not.
Person 2 defends the exact opposite argument. However lets grant that Person 2 is cherry picking their facts. When Person 1 argues that 'Pr(A/E) > Pr(T/E)' Person 1 is arguing with a set of evidence E that consists of 10 facts, but Person 2 is arguing with a set of evidence E1 that consists of only 5 facts.
If the actual evidence consists of the 10 facts rather than merely the 5, then Person 2 can come up with an unjustified degree of belief in T since the actual evidence is E rather than E1. This is a problem that many people might have when making a cumulative case for or against theism.
For example let's grant that the evidence to be considered in this world was that minds depend on brains, the roles of biological pain and pleasure, the flourishing of humans, the flourishing of non humans, and the existence of rational beings.
The theist might reason that the probability of rational beings existing given theism is extremely high, and is much greater than the probability of rational beings given atheism. But the theist stops there. He does not think to factor in the probability of the total set of evidence given theism, rather the theist makes use of a small subset of the evidence. But by doing so the theist might unjustly find that theism is much more probable than atheism, even if all things considered atheism is more probable given the total set of evidence. If one portion of the evidence greatly favoured theism over atheism but the rest did not, then this could make the probability of theism given the evidence much lower, possibly in such a way that belief in theism is not justified at all.
