This is the same thought process that was followed by hundreds of Ex-Christadelphians when their faith crumbled before they stopped attending Christadelphian ecclesias or resigned from fellowship.
For Christadelphianism to be true the Bible has to be inspired by God and therefore sensibly written and not riddled with mistakes and contradictions that show only human authorship. Christadelphians are increasingly agreeing with us that there is something very wrong with the Bible. It is full of mistakes. Biblical apologetics are merely a temporary bailing out measure in a rapidly sinking boat. Modern science, textural analysis, reason, common-sense and even philosophy have shown the paranormal origin of the Bible to be a proposition that strains credulity.
By Ken Gilmore
The next chapter in Peter Enns' series in which Biblical scholars from an evangelical / fundamentalist background relate the moment when their detailed study of the Bible led them to acknowledge that a literalist / fundamentalist reading of the Bible was untenable comes from John Byron, professor of NT at Ashland Theological Seminary. His moment came during a Bible college discussion of Mark 2:23-37 which when read literally appears contradicts 1 Sam 21:1-9 both in the name of the High Priest, and the amount of people present during the narrative.
This is exactly the same passage that triggered Bart Ehrman's drift away from conservative to liberal Christianity:
In my paper for Professor Story, I developed a long and complicated argument to the effect that even though Mark indicates this happened “when Abiathar was the high priest,” it doesn’t really mean that Abiathar was the high priest, but that the event took place in the part of the scriptural text that has Abiathar as one of the main characters. My argument was based on the meaning of the Greek words involved and was a bit convoluted. I was pretty sure Professor Story would appreciate the argument, since I knew him as a good Christian scholar who obviously (like me) would never think there could be anything like a genuine error in the Bible. But at the end of my paper he made a simple one-line comment that for some reason went straight through me. He wrote: “Maybe Mark just made a mistake.” I started thinking about it, considering all the work I had put into the paper, realizing that I had had to do some pretty fancy exegetical foot-work to get around the problem, and that my solution was in fact a bit of a stretch. I finally concluded, “Hmm…maybe Mark did make a mistake.”
Once I made that admission, the floodgates opened. For if there could be one little, picayune mistake in Mark 2, maybe there could be mistakes in other places as well. Maybe, when Jesus says later in Mark 4 that the mustard seed is “the smallest of all seeds on the earth,” maybe I don’t need to come up with a fancy explanation for how the mustard seed is the smallest of all seeds when I know full well it isn’t. And maybe these “mistakes” apply to bigger issues. Maybe when Mark says that Jesus was crucified the day after the Passover meal was eaten (Mark 14:12; 15:25) and John says he died the day before it was eaten (John 19:14)—maybe that is a genuine difference. Or when Luke indicates in his account of Jesus’s birth that Joseph and Mary returned to Nazareth just over a month after they had come to Bethlehem (and performed the rites of purification; Luke 2:39), whereas Matthew indicates they instead fled to Egypt (Matt. 2:19–22)—maybe that is a difference. Or when Paul says that after he converted on the way to Damascus he did not go to Jerusalem to see those who were apostles before him (Gal. 1:16–17), whereas the book of Acts says that that was the first thing he did after leaving Damascus (Acts 9:26)—maybe that is a difference. 
Ehrman did not become an agnostic because of that episode. Rather, it was the problem of suffering which catalysed his loss of faith.  However, it is interesting to compare his response with Byron's:
The earliest example occurred in Bible College. The instructor was discussing Mark 2:23-27, which narrates the challenge of the Pharisees to Jesus over his disciples picking grain on the Sabbath. Jesus responds to their question by referring to the story in 1 Samuel 21:1-9 of David and his men eating the consecrated bread from the tabernacle.
The problem, however, as I pointed out to my teacher, is that Jesus got it wrong. The story in 1 Samuel 21 relates how David fled from Saul alone. When he stops at the tabernacle and asks Ahimelek for help the priest enquires why David is alone. David seems to lie when saying that his men well meet him later (v. 2).
Moreover, Mark has the wrong priest. In 2:26 Jesus states that the priest was Abiather, but 1 Samuel 21 clearly states that it was Ahimelek.
When I raised these points with the teacher, in the middle of class (I wasn’t as tactful then) he looked at me with confusion. He had never noticed these discrepancies before. I was asked politely to be quiet. Years later I was pleasantly surprised to read that it was this very same passage in Mark that signaled the beginning of Bart Ehrman’s faith journey, although he and I are, in many ways, in very different places.
In the end, of course, it wasn’t just one problem like Mark 2:26 that caused me to reexamine how I understood the Bible—but it was a hook and it began a process. Over time numerous passages forced me to conclude eventually that the Bible wasn’t a history book, meaning the authors were not trying to give me a blow-by-blow account from creation to the end of the first century.
Instead I came to realize that the Bible was first and foremost a theological book that contains history and uses history to direct me towards God. I would come to realize more and more that true faith—the faith God calls us to—was not focused on the Bible, but on the God to whom the Bible bears witness. (Emphasis in original) 
Did Jesus really get it wrong? Did Mark really have the wrong priest? Not a few NT scholars have invested considerable time to reconcile this problem. NT textual critic Dan Wallace has proposed that we "take the prepositional phrase as meaning “in the days of Abiathar the high priest.”  He is honest enough to admit that more work is needed on this problem, and acknowledges that over 120 years after 19th century NT scholar Thomas Lindsay acknowledged that none of the then proposed solutions were satisfactory "if Lindsay were to rise from the dead he’d repeat his complaint verbatim!" 
For any fundamentalist wedded to an extreme view of biblical inspiration and authority which insists that every word of the Bible was dictated by God directly into the minds of the human writers, and that it is the ultimate authority in all fields of knowledge, problems such as these pose a huge threat to their views on the inspiration and authority of the Bible. Invariably, that results in the theological equivalent of epicycles being constructed in order to preserve their theological paradigm from falsification. Wallace's observations on this point hold just as true for Christadelphian fundamentalists as they do for evangelicals:
In the least, it is imperative that we not frontload our presuppositions to such an extent that we don’t listen to the text. Evangelicalism is populated with all sorts of academic gatekeepers whose theological a priori drives their investigation and determines its results. The tragic irony is that such people never really learn from the text, for they have already decided what it will tell them. 
The real tragedy comes when such fundamentalists are no longer able to keep on maintaining an ever-increasing number of ad-hoc rationalisations to protect their view of Biblical inspiration and authority
The deepest tragedy along these lines is when someone never differentiates doctrinal commitments, for this leaves him wide open to chucking his entire belief system when the weakest link is broken. From experience, I can tell you that this “domino view of doctrine” is altogether too prevalent and has been the ruin of a great many evangelical doctoral students. 
What separates the fundamentalists who have managed to face such challenges and escape fundamentalism while remaining believers from those whose crashed into unbelief? It is of course impossible to propose a one-size-fits-all solution, but Wallace is arguably on the right track when he says that we should "embrace the Bible as a witness to the great acts of God in history, especially to the Christ-event. This is enough for salvation." From this it follows that if we see problems outside of this area which are not amenable to solution, we should have the wisdom to recognise that they do not affect salvation, and not obsess over 'mistakes' and 'errors' and strive to harmonise every 'problem'.
1. Ehrman B Misquoting Jesus (2009: HarperCollins) p 9-10
2. Ehrman B God's Problem (2009: HarperCollins) p 1-3
3. Byron J "aha" moments: biblical scholars tell their stories (2): John Byron Peter Enns: Rethinking Biblical Christianity June 27th 2014
4. Wallace D "Mark 2:26 and the Problem of Abiathar" Evangelical Theological Society Southwest Regional Meeting, Dallas Theological Seminary March13, 2004