A bad argument is bad even if a Christian makes it, and here are two bad arguments that Christians sometimes make. They don’t make these arguments because they are Christians, just because they are not thinking well.
Sometimes, when backed into an intellectual corner, Christians will say, “Well, it is all a mystery. I cannot understand it, but I believe it.”
Of course, some things are beyond my capacity to understand (in my case, modern physics), and I have to do the best I can to find good experts I can trust. Appropriate modesty about my abilities to understand hard things is good.
If something I assert seems wrong, however, then calling it a mystery to relieve the pressure I feel is not good. I should have good reason to believe an idea, even if that reason is only my trust of an expert. If I am presented with something that makes my views seem unreasonable and I understand that attack, then a resort to “mystery” language is nothing more than intellectual cowardice.
If I am talking to an atheist, for example, I will almost certainly hear things that do not fit what I believe. Yet, if I understand their attack, then I must try to respond to it according to my level of understanding. My confusion is not a “mystery,” but simply a sign of my current mental defeat.
There is nothing wrong with failing to answer an argument, but there is something wrong with hiding behind “mystery” to avoid the consequences. It's much, much better to say, “You win that point, and I need to think about that. Meanwhile, I remain a Christian for the following reasons and because of the following experiences...”
Of course, if in the end I cannot answer the argument to my level of comprehension, then I should change my mind. In some rare cases, that might mean changing my religion or abandoning religion altogether, but in most cases it usually only necessitates modifying my views.
For example, if I happened to be a Christian who believed that only the King James Translation of the Bible is inspired, then an atheist might attack my beliefs by pointing to changes in the text of the King James over the centuries. If I was unable to answer those attacks (and I doubt I could), it would not mean that I needed to become an atheist, but merely that I needed to abandon my “King James only” version of Christianity.
This is important to remember, since without the memory of it, Christians can often end up with unduly fragile systematic beliefs. My view is that the Bible is without error in every respect (including in its historical and scientific statements), but good Christians like C.S. Lewis were traditional Christians (very conservative ones!) without that belief. Therefore, I can take heart. If I hear an argument about “Bible errors” from a secularist, I can remember that it is only an attack on that particular belief, and not on Christianity as a whole.
Fundamentally speaking, it is always possible that my entire worldview would have to change at some point, but such a need will always be rare if I have embraced a complex, ancient, and intellectually rigorous point of view.
There are some details of religion that are as far beyond my intellectual capacity as modern physics is, but my goal is to do the best I can. “Mystery” exists where human comprehension fails, but it does not exist where my intellectual fortitude fails. Fog is not the same as “mystery”; let's not hide from our problems by misusing a wonderful word.