K. E. Bailey, K. E. (2008). (Jesus through Middle Eastern Eyes: Cultural Studies in the Gospels (p. 230). Downers Grove, IL: IVP Academic, 2000) argues for the inclusion of 7:53-8:11 along the same lines as St. Augustine. He argues that at that time people hire copyists. if they didn't want the copyist to include the story because they didn't want their daughters to read it, they could tell the copyist to leave it out.
However, if you read 7:53-8:11 in the original language, the Greek is different and more difficult than the Greek in the rest of the Gospel of John. That along with the overwhelming lack of inclusion in the early manuscripts make it unlikely that this passage was originally in the Gospel of John. Most likely it was a true story preserved by oral tradition before being added to the Gospel of John.
Appendix
This quote from Bruce Metzger's commentary is in the Appendix because of the length of technical information.
7:53–8:11 Pericope of the Adulteress
The evidence for the non-Johannine origin of the pericope of the adulteress is overwhelming. It is absent from such early and diverse manuscripts as 𝔓66, א B L N T W X Y Δ Θ Ψ 0141 0211 22 33 124 157 209 788 828 1230 1241 1242 1253 2193 al. Codices A and C are defective in this part of John, but it is highly probable that neither contained the pericope, for careful measurement discloses that there would not have been space enough on the missing leaves to include the section along with the rest of the text. In the East the passage is absent from the oldest form of the Syriac version (syrc, and the best manuscripts of syrp), as well as from the Sahidic and the sub-Achmimic versions and the older Bohairic manuscripts. Some Armenian manuscripts and the Old Georgian version omit it. In the West the passage is absent from the Gothic version and from several Old Latin manuscripts (ita, *, ). No Greek Church Father prior to Euthymius Zigabenus (twelfth century) comments on the passage, and Euthymius declares that the accurate copies of the Gospel do not contain it.
When one adds to this impressive and diversified list of external evidence the consideration that the style and vocabulary of the pericope differ noticeably from the rest of the Fourth Gospel (see any critical commentary), and that it interrupts the sequence of 7:52 and 8:12 ff., the case against its being of Johannine authorship appears to be conclusive.
At the same time the account has all the earmarks of historical veracity. It is obviously a piece of oral tradition which circulated in certain parts of the Western church and which was subsequently incorporated into various manuscripts at various places. Most copyists apparently thought that it would interrupt John’s narrative least if it were inserted after 7:52 (D E (F) G H K M U Γ Π 28 700 892 al). Others placed it after 7:36 (ms. 225) or after 7:44 (several Georgian mss) or after 21:25 (1 565 1076 1570 1582 armmss) or after Lk 21:38 (f ). Significantly enough, in many of the witnesses that contain the passage it is marked with asterisks or obeli, indicating that, though the scribes included the account, they were aware that it lacked satisfactory credentials.
Sometimes it is stated that the pericope was deliberately expunged from the Fourth Gospel because Jesus’ words at the close were liable to be understood in a sense too indulgent to adultery. But, apart from the absence of any instance elsewhere of scribal excision of an extensive passage because of moral prudence, this theory fails “to explain why the three preliminary verses (vii 53; viii 1–2), so important as apparently descriptive of the time and place at which all the discourses of c. viii were spoken, should have been omitted with the rest” (Hort, “Notes on Select Readings,” pp. 86 f.).
Although the Committee was unanimous that the pericope was originally no part of the Fourth Gospel, in deference to the evident antiquity of the passage a majority decided to print it, enclosed within double square brackets, at its traditional place following Jn 7:52.
Inasmuch as the passage is absent from the earlier and better manuscripts that normally serve to identify types of text, it is not always easy to make a decision among alternative readings. In any case it will be understood that the level of certainty ({A}) is within the framework of the initial decision relating to the passage as a whole.
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Metzger, B. M., United Bible Societies. (1994). A textual commentary on the Greek New Testament, second edition a companion volume to the United Bible Societies’ Greek New Testament (4th rev. ed.) (pp. 187–189). London; New York: United Bible Societies.