If the bible is the inerrant word of god, how do Christians reconcile the obvious edits to the word?

Protestants have justified it by saying that story really happened and we know this because it has ancient origins, God just added it to his book later. Protestants sometimes speak about the Bible like it's a living document which God can add to, much like Americans see the Constitution as a living document which can be amended. Which is ironic, because the Bible itself says that it's a huge sin for anyone to add to it. Kinda funny, since so many people have added to it through the years.
As for Roman Catholics and the Eastern Orthodox, they say the Bible is imperfect because it was collected by humans. What really matters to them is tradition. Also funny, because their traditions have changed over the centuries.