The basic concept behind the Masoretic-Greek Hypothesis (hereafter MGH) could be summarized as going to the source. Let's face it: the Christianity that many believers argue is indeed a moving target. Although I think it's an intellectual cop-out, I sympathize with atheists and unbelieving skeptics when they accuse believers of trotting out Courtier's Replies. Who wants to get bogged down trying to harmonize all the differing opinions of mainline religions and lesser sects, each of whom claim to be eating from the same salad bar called the Bible? Certainly not me. On the other hand, I sympathize with believers when they accuse atheists and unbelieving skeptics of gross negligence in their characterizations of religion.
M is the work of the Masoretes, Jewish scribes and scripture scholars living roughly 3,000 years ago in what today would probably be Jerusalem, Tiberius or even what would be considered Iraq (then Babylon, Babylonia). M represents the Hebrew rendition of the Tanakh. Many if not most Protestant and Catholic Bibles sample from M, as does the Septuagint (39 books of the OT + select Apocrypha) from which the New Testament writers sampled. G is the New Testament derived as described. This way, we arguably start as close to the actual events and oral traditions as possible, then apply our collective powers of reason to ascertain the set of reasonably permissible predictions.
This means we'll inevitably discuss Old Testament Hebrew and New Testament Greek, lexicon that may be foreign, unwelcome or intimidating for some. We're bound for some rough spots for sure, as many a discussion between atheists and believers derails around this point, but I have faith in our combined powers of reason.