The doctrine of the divine inspiration of the Bible holds that since God is absolute Truth, His Word, the Bible, must be "infallible" (without error) in the original manuscripts. Of course, many errors have crept into the various manuscript traditions, so few Christians would argue for the infallibility of any particular translation.
It seems to me that someone who claims to be a Christian yet denies the infallibility of the Bible will sooner or later face a crisis of authority. That is to say, they may want to defend their Faith, and do not want to accept the attacks of the critics against Christianity, yet they have no sure authority with which to counter such arguments.
The rejection of the authority of the "Old Testament Stories" because they are "thousands of years old" is a problematic position to hold if one intends to contend for any lingering authority in the Scriptures, for of course, the New Testament "stories" are likewise very "old."
Likewise, if the Old Testament stories are to be rejected as authoritative because they "passed through barbs and word of mouth for the majority of their existence," the same could be said for the New Testament stories.
It is rather like the poor fellow stuck out in the middle of the ocean who has inadvertently pulled the plug in his life raft and yet is clinging to the hope that at least some part of the raft will remain inflated. In the same sense, Truth is a seamless garment: if you deny the infallibility of the Scriptures and yet attempt to "retain" those parts which you deem to be authoritative, you will soon find that there is no part of Scripture which is "safe" from the attacks of the critics. And you will be left with no persuasive argument against them other than your subjective impressions as to what is "truly" the Word of God.
But will that get you through in times of crisis? I for one could not trust in my own subjective opinion. Isn't it odd that we should reject the authority of God's Word on the basis of our own very limited, fallible judgment?
I have a terminal degree in Theology and at one time was very conversant in the issues and views regarding Biblical infallibility/inerrancy. I have also taught Biblical history and archaeology on site in Israel. My considered opinion is that those who reject Biblical infallibility do so because they have chosen to accept it - for whatever reason - "by faith." That is to say, few if any have actually conducted primary research as to the historical and archaeological evidences for the historicity of the text.
More often, they choose to reject the full authority of Scripture because they do not want to be seen as an uniformed and gullible Christian. In short, they are willing to jettison the Christian belief that the Bible is the Word of God in order to retain (what they believe to be) the respect of those around them.
But this is a fool's errand, for nothing short of the total repudiation of the Truth of Christianity and the Bible will make you "respectable" in the eyes of those who hate the Gospel.
On the basis of my study and experience, I can wholeheartedly affirm the full and complete authority of the Bible - including the book of Genesis. Yes, of course there are difficult passages and even apparent (though not proven actual) contradictions, but like the bard who confessed regarding his Love who had been wrongly accused of unfaithfulness, "I believed in you even when I knew you were guilty..."
Infallibility does not equal literal translation and literal intent. For instance, back to the subject, the earth is not 6000 yeard old. It just isnt. It can be said beyond a reasonable doubt. You are the one facing a xrisis of authority because your interpretation blows up your entire faith because the earth is 6 billion years old. It is sad for you because the fact that the earth is 6 billion years old is really inconsequential unless you are an evangelical. Perhaps you should consider Catholicism or Episcopalianism and these mundane nuances wouldnt cause you such crises.