In defending what we believe, we can't let ourselves retreat into positions that undermine the Gospel.
If you spent way too much time in school like I did, you may have encountered "rules of inference," a collection of different ways to validly judge the truth of a claim based on what else you know to be true. A personal favorite of mine is "reductio ad absurdum," which is Latin because I guess "reduction to absurdity" loses some of the charm or something. This rule just says that you can discard a statement if it necessarily implies something that you absolutely know to be false or creates a contradiction.
There's a classic example in math: suppose there's a biggest number and call it "N." Since it's a number, we can add to it, so we can make "N+1." But N+1 is bigger than N, so N can't be the biggest number. The statement creates a contradiction, therefore it is false and there is no biggest number.
If you're not a math person, though, consider this example: your father appears to be asleep during a movie, so you try to wake him by addressing him. Eventually, you just shout "Dad!" and he jumps before telling you "I was just resting my eyes." Alright, assume he's right. If he was just resting his eyes, his other senses were active. Therefore, he could hear what was going on before you shouted. Since he could hear, he shouldn't have jumped halfway to the Moon when you shouted. But he did, therefore he was not merely resting his eyes.
As with any rule of inference, we have to be careful as to whether it really applies. Not all statements should be taken so absolutely that such a reduction is possible, and you should ensure that all your logical steps are solid - the above example might not actually work if your father is as deaf as a stone. But it is a handy rule to sort out untruths by chasing down their implications.
Human silliness, however, produces a mirror version of reduction to absurdity. In reduction, we start with a premise, determine what it must imply, and test the conclusion to test our premise. In the mirror version, we start with a conclusion, determine what argument might lead to that conclusion, and then assert the argument's premise. That is, to defend an idea, we start clinging to arguments for it regardless of whether they make any sense.
You can see this reasoning in politics all the time. I like candidate X because he isn't candidate Y, but that's not very inspiring, so I need arguments for why candidate X is the best candidate. Clearly, uh, he's a great person and an upright human being! I will then spend the rest of the electoral process clinging to that premise no matter what evidence is thrown at me - it's either all fabricated, or exaggerated, or who hasn't ruined thousands of lives for personal advantage?
Thus, I call this mirror reasoning "retreat to absurdity." Our human nature can be so attached to a belief that it will fall back into whatever fortress it thinks can defend that belief, even if that leads us to adopt absolutely ridiculous ideas.
Naturally, with how essential our spirituality is to who we are, theology is no exception. Three examples stand out to me:
1. How NOT to argue against Mary as Mother of God
The title of "Mother of God" is a fairly old one, especially in its Greek form of "Theotokos," literally "the God-Bearer." Naturally, some bristle at such a grandiose title for a mere creature, especially since one might misinterpret it to mean something like "Mother of the Holy Trinity" as though Mary was the creator of the Creator. However, the logic for this title is pretty straightforward: Mary is the mother of Jesus, who is God in the flesh, therefore Mary is the Mother of God.
There are undoubtedly other arguments against the title, but at this point critics frequently fall back into a classic argument advanced by one of the most prominent figures in the fifth century Church, Patriarch Nestorius of Constantinople: there is sufficient separation between the humanity and divinity of Jesus that Mary could be the mother of his human nature but not his divine nature. This created quite the controversy in its time, and it's frequently revived to this day as an argument, implicit or explicit, against giving Mary such a title.
But what's the problem with this argument? We absolutely ought to distinguish between the human and divine natures of Jesus, but we also have to recognize that they are truly united in one person. As John's Gospel says, "the Word became flesh," not "the Word partnered up with flesh." Why does this matter? Well, suppose we have a human Jesus and a divine Jesus, and what is true about one is not necessarily true about the other...
Which Jesus died for us on the Cross?
Seriously, if the divinity of Jesus is so divorced from his humanity that it can't truly have a mother, how can we believe that it could die for us? And if his divinity was not offered up, then the offering does not have infinite value, and we've let our discomfort with every generation calling Mary blessed turn the Gospel into a scam. We've retreated into absurdity.
2. How NOT to argue against prayer to saints and angels
The historical practice of seeking the intercession of heavenly saints is a common bone of contention with Christian traditions which arose out of the Reformation. From an outside perspective, it might seem like worship (i.e., idolatry!), competition with prayer to God, or imposing extra mediators on the New Covenant.
Arguments over the controversy frequently involve attempts to explain how these concerns do not apply to the authentic practice. I won't get into everything involved in those arguments here or the many others that could be raised, but here's what I frequently hear when those objections have been answered: It doesn't matter, because heavenly saints can't hear you, because they're dead.
Dead as in asleep on earth but alive in Paradise? Sometimes yes, and that's a fairly simple case - Paul tells us we are surrounded by a cloud of witnesses composed of such, and Revelation, besides having John witness earthly events from heaven, depicts angels and saints offering up the prayers of the Church on earth. They most certainly can hear us!
But sometimes the answer is no - they're not asleep, they are dead, period.
Putting aside all the Biblical depictions of the dead being conscious (righteous or not!), this mortalism reasserts the authority of death over the Christian, even if it acknowledges an expiration date at the Resurrection. Where, oh Death, is thy sting? Apparently still there!
However much one might be uncomfortable with the communion of saints transcending the grave, we must never let it nullify the eternal life Jesus offers us - that's an absurdity we must never retreat to!
3. How NOT to argue against the authority of Tradition or the Church
Central to the divisions among Christians is what authority has been established by God that we might know and love him truly - are the Scriptures God-breathed inerrant truth, are the practices and beliefs handed down from the Apostles binding, and does the Spirit guide a living body to teach and minister? The Catholic claim is yes, yes, and yes.
There are many ways Protestant Christians challenge those last two affirmatives. Do we actually possess the practices and beliefs of the Apostles? If we did, are the Apostles themselves infallible? Is the Spirit actually guiding a particular body? Is the Spirit actually preserving such a body from error? Can any body claim a visible expression for the mystical body of Christ? Can any of the above constitute something comparable to Scripture? Etc., etc., and those are fair questions worthy of debate.
But then there's another tack. You don't need to grapple with Catholic claims about authority if you just assert that the original Church and its Tradition disappeared from the face of the earth.
After the Reformation, a few radical sects made this assertion, well beyond the typical claims of gradual corruption made by Luther, Calvin, and others. In particular, Jehovah's Witnesses and Mormons attach themselves to this "Great Apostasy" as a foundational belief.
Right off the bat, this should set off alarm bells. The ministry of Jesus Christ should be the axis around which salvation history turns - once he has established his Church, the gates of hell should not be able to claim that kind of triumph against it! He promised he would be with us to the end of the world and that his Spirit would remind us of all he taught us - is Our Lord really just Our Liar?
There's also a practical problem - when did this happen? The classic answer is the reign of the Roman Emperor Constantine, who decriminalized Christianity in 313 and presided over the Council of Nicaea in 325, but whose own commitment to Christianity could be shaky. So, some argue, Constantine fundamentally upended original Christianity and infused it with paganism! That's why Catholics pray to/for the dead, think the Lord's Supper is literal and sacrificial, and follow a clerical hierarchy!
When Joseph Smith "translated" a record of how Church leaders went rogue in pursuit of fancy clothes, he likely was not familiar with the fatal flaw of this theory: the time between the New Testament and Constantine isn't a black box. We have loads of evidence about what Christians of the time believed and practiced, especially in the form of letters, essays, and even entire books written by Christians.
So what do you do when you discover the Christian Tertullian describing at the dawn of the 200s how Christians offer the Eucharist on behalf of the departed on the anniversary of their passing, what do you do? You have to push the great apostasy back... and you keep pushing as you read earlier and earlier documents containing supposed corruptions. Next thing you know, you're pushing the date back into the life of the Apostle John and starting to undermine the compilation of the New Testament.
It might take someone time to swallow the idea that God might work so powerfully through a community that it might be called the pillar and foundation of the truth, but professing that God abandoned his faithful to paganism for over a thousand years is a retreat into absurdity.